{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T05:53:25Z","timestamp":1775541205437,"version":"3.50.1"},"reference-count":6,"publisher":"American Mathematical Society (AMS)","issue":"4","license":[{"start":{"date-parts":[[2004,7,17]],"date-time":"2004-07-17T00:00:00Z","timestamp":1090022400000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proc. Amer. Math. Soc."],"abstract":"<p>\n                    Let\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper U Subscript n Baseline left-parenthesis q right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi>U<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi>n<\/mml:mi>\n                              <\/mml:mrow>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>q<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">U_{n}(q)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    denote the unitriangular group of degree\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"n\">\n                        <mml:semantics>\n                          <mml:mi>n<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">n<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    over the finite field with\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"q\">\n                        <mml:semantics>\n                          <mml:mi>q<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">q<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    elements. In a previous paper we obtained a decomposition of the regular character of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper U Subscript n Baseline left-parenthesis q right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi>U<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi>n<\/mml:mi>\n                              <\/mml:mrow>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>q<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">U_{n}(q)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    as an orthogonal sum of basic characters. In this paper, we study the irreducible constituents of an arbitrary basic character\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"xi Subscript script upper D Baseline left-parenthesis phi right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi>\n                                \u03be\n                                \n                              <\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                  <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                    <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">D<\/mml:mi>\n                                  <\/mml:mrow>\n                                <\/mml:mrow>\n                              <\/mml:mrow>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>\n                              \u03c6\n                              \n                            <\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\xi _{{\\mathcal {D}}}(\\varphi )<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper U Subscript n Baseline left-parenthesis q right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi>U<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi>n<\/mml:mi>\n                              <\/mml:mrow>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>q<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">U_{n}(q)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . We prove that\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"xi Subscript script upper D Baseline left-parenthesis phi right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi>\n                                \u03be\n                                \n                              <\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                  <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                    <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">D<\/mml:mi>\n                                  <\/mml:mrow>\n                                <\/mml:mrow>\n                              <\/mml:mrow>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>\n                              \u03c6\n                              \n                            <\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\xi _{ {\\mathcal {D}}}(\\varphi )<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is induced from a linear character of an algebra subgroup of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper U Subscript n Baseline left-parenthesis q right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi>U<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi>n<\/mml:mi>\n                              <\/mml:mrow>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>q<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">U_{n}(q)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , and we use the Hecke algebra associated with this linear character to describe the irreducible constituents of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"xi Subscript script upper D Baseline left-parenthesis phi right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi>\n                                \u03be\n                                \n                              <\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                  <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                    <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">D<\/mml:mi>\n                                  <\/mml:mrow>\n                                <\/mml:mrow>\n                              <\/mml:mrow>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>\n                              \u03c6\n                              \n                            <\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\xi _{{\\mathcal {D}}}(\\varphi )<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    as characters induced from an algebra subgroup of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper U Subscript n Baseline left-parenthesis q right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi>U<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi>n<\/mml:mi>\n                              <\/mml:mrow>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>q<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">U_{n}(q)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . Finally, we identify a special irreducible constituent of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"xi Subscript script upper D Baseline left-parenthesis phi right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi>\n                                \u03be\n                                \n                              <\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                  <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                    <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">D<\/mml:mi>\n                                  <\/mml:mrow>\n                                <\/mml:mrow>\n                              <\/mml:mrow>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>\n                              \u03c6\n                              \n                            <\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\xi _{{\\mathcal {D}}}(\\varphi )<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , which is also induced from a linear character of an algebra subgroup. In particular, we extend a previous result (proved under the assumption\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"p greater-than-or-equal-to n\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>p<\/mml:mi>\n                            <mml:mo>\n                              \u2265\n                              \n                            <\/mml:mo>\n                            <mml:mi>n<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">p \\geq n<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    where\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"p\">\n                        <mml:semantics>\n                          <mml:mi>p<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">p<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is the characteristic of the field) that gives a necessary and sufficient condition for\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"xi Subscript script upper D Baseline left-parenthesis phi right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi>\n                                \u03be\n                                \n                              <\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                  <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                    <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">D<\/mml:mi>\n                                  <\/mml:mrow>\n                                <\/mml:mrow>\n                              <\/mml:mrow>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>\n                              \u03c6\n                              \n                            <\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\xi _{{\\mathcal {D}}}(\\varphi )<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    to have a unique irreducible constituent.\n                  <\/p>","DOI":"10.1090\/s0002-9939-03-07143-0","type":"journal-article","created":{"date-parts":[[2004,4,21]],"date-time":"2004-04-21T12:43:50Z","timestamp":1082551430000},"page":"987-996","source":"Crossref","is-referenced-by-count":14,"special_numbering":"538","title":["Hecke algebras for the basic characters of the unitriangular group"],"prefix":"10.1090","volume":"132","author":[{"given":"Carlos","family":"Andr\u00e9","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2003,7,17]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1006\/jabr.1995.1187","article-title":"Basic characters of the unitriangular group","volume":"175","author":"Andr\u00e9, Carlos A. M.","year":"1995","journal-title":"J. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0021-8693","issn-type":"print"},{"key":"2","doi-asserted-by":"crossref","unstructured":"C. A. M. Andr\u00e9, Basic characters of the unitriangular group (for arbitrary primes), Proc. Amer. Math. Soc. 130, no. 7, (2002), 1943\u20131954.","DOI":"10.1090\/S0002-9939-02-06287-1"},{"key":"3","series-title":"Pure and Applied Mathematics","isbn-type":"print","volume-title":"Methods of representation theory. Vol. I","author":"Curtis, Charles W.","year":"1981","ISBN":"https:\/\/id.crossref.org\/isbn\/0471189944"},{"key":"4","series-title":"De Gruyter Expositions in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1515\/9783110809237","volume-title":"Character theory of finite groups","volume":"25","author":"Huppert, Bertram","year":"1998","ISBN":"https:\/\/id.crossref.org\/isbn\/3110154218"},{"issue":"3","key":"5","doi-asserted-by":"publisher","first-page":"708","DOI":"10.1006\/jabr.1995.1325","article-title":"Characters of groups associated with finite algebras","volume":"177","author":"Isaacs, I. M.","year":"1995","journal-title":"J. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0021-8693","issn-type":"print"},{"issue":"2","key":"6","doi-asserted-by":"publisher","first-page":"704","DOI":"10.1006\/jabr.1997.7311","article-title":"Conjugacy in groups of upper triangular matrices","volume":"202","author":"Isaacs, I. M.","year":"1998","journal-title":"J. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0021-8693","issn-type":"print"}],"container-title":["Proceedings of the American Mathematical Society"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/proc\/2004-132-04\/S0002-9939-03-07143-0\/S0002-9939-03-07143-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/proc\/2004-132-04\/S0002-9939-03-07143-0\/S0002-9939-03-07143-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T19:41:15Z","timestamp":1773344475000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/proc\/2004-132-04\/S0002-9939-03-07143-0\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,7,17]]},"references-count":6,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2004,4]]}},"alternative-id":["S0002-9939-03-07143-0"],"URL":"https:\/\/doi.org\/10.1090\/s0002-9939-03-07143-0","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6826","0002-9939"],"issn-type":[{"value":"1088-6826","type":"electronic"},{"value":"0002-9939","type":"print"}],"subject":[],"published":{"date-parts":[[2003,7,17]]}}}