{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T03:25:25Z","timestamp":1773372325787,"version":"3.50.1"},"reference-count":12,"publisher":"American Mathematical Society (AMS)","issue":"7","license":[{"start":{"date-parts":[[2003,1,17]],"date-time":"2003-01-17T00:00:00Z","timestamp":1042761600000},"content-version":"am","delay-in-days":365,"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 (upper) 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\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper F Subscript q\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">F<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi>q<\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {F}_{q}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    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 this paper we consider the basic (complex) characters 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 prove that every irreducible (complex) 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                    is a constituent of a unique basic character. This result extends a previous result which was proved by the author 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\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper F Subscript q\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">F<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi>q<\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {F}_{q}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    .\n                  <\/p>","DOI":"10.1090\/s0002-9939-02-06287-1","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:28Z","timestamp":1027707268000},"page":"1943-1954","source":"Crossref","is-referenced-by-count":48,"special_numbering":"517","title":["Basic characters of the unitriangular group (for arbitrary primes)"],"prefix":"10.1090","volume":"130","author":[{"given":"Carlos","family":"Andr\u00e9","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2002,1,17]]},"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"},{"issue":"1","key":"2","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"},{"issue":"1","key":"3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1006\/jabr.1997.7258","article-title":"The regular character of the unitriangular group","volume":"201","author":"Andr\u00e9, Carlos A. M.","year":"1998","journal-title":"J. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0021-8693","issn-type":"print"},{"key":"4","doi-asserted-by":"crossref","unstructured":"C. A. M. Andr\u00e9, The basic character table of the unitriangular group, J. Algebra 241 (2001), 437\u2013471.","DOI":"10.1006\/jabr.2001.8734"},{"key":"5","isbn-type":"print","first-page":"65","article-title":"Irreducible characters of finite algebra groups","author":"Andr\u00e9, Carlos A. M.","year":"1999","ISBN":"https:\/\/id.crossref.org\/isbn\/9728564198"},{"key":"6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1515\/crll.1940.181.1","article-title":"Untersuchungen \u00fcber reinverzweigte Erweiterungen diskret bewerteter perfekter K\u00f6rper","volume":"181","author":"Arf, Cahit","year":"1939","journal-title":"J. Reine Angew. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0075-4102","issn-type":"print"},{"key":"7","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":"8","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"},{"key":"9","unstructured":"I. M. Isaacs, Character theory of finite groups, Dover, New York, 1994."},{"issue":"3","key":"10","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":"11","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"},{"key":"12","first-page":"9","article-title":"Discrete series and the unipotent subgroup","volume":"28","author":"Lehrer, G. I.","year":"1974","journal-title":"Compositio Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0010-437X","issn-type":"print"}],"container-title":["Proceedings of the American Mathematical Society"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/proc\/2002-130-07\/S0002-9939-02-06287-1\/S0002-9939-02-06287-1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/proc\/2002-130-07\/S0002-9939-02-06287-1\/S0002-9939-02-06287-1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T16:43:22Z","timestamp":1773333802000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/proc\/2002-130-07\/S0002-9939-02-06287-1\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,1,17]]},"references-count":12,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2002,7]]}},"alternative-id":["S0002-9939-02-06287-1"],"URL":"https:\/\/doi.org\/10.1090\/s0002-9939-02-06287-1","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":[[2002,1,17]]}}}