{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T15:18:27Z","timestamp":1776784707418,"version":"3.51.2"},"reference-count":9,"publisher":"American Mathematical Society (AMS)","issue":"252","license":[{"start":{"date-parts":[[2006,3,24]],"date-time":"2006-03-24T00:00:00Z","timestamp":1143158400000},"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":["Math. Comp."],"abstract":"<p>\n                    We study the realizability over\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper R\">\n                        <mml:semantics>\n                          <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                            <mml:mi mathvariant=\"double-struck\">R<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {R}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    of representations of the group\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper U left-parenthesis n right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>U<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">U(n)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    of upper-triangular\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"n times n\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:mo>\n                              \u00d7\n                              \n                            <\/mml:mo>\n                            <mml:mi>n<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">n \\times n<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    matrices over\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper F 2\">\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:mn>2<\/mml:mn>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {F}_2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . We prove that all the representations of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper U left-parenthesis n right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>U<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">U(n)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    are realizable over\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper R\">\n                        <mml:semantics>\n                          <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                            <mml:mi mathvariant=\"double-struck\">R<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb R<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    if\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"n less-than-or-equal-to 12\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:mo>\n                              \u2264\n                              \n                            <\/mml:mo>\n                            <mml:mn>12<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">n \\leq 12<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , but that if\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"n greater-than-or-equal-to 13\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:mo>\n                              \u2265\n                              \n                            <\/mml:mo>\n                            <mml:mn>13<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">n \\geq 13<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    ,\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper U left-parenthesis n right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>U<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">U(n)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    has representations not realizable over\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper R\">\n                        <mml:semantics>\n                          <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                            <mml:mi mathvariant=\"double-struck\">R<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb R<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . This theorem is a variation on a result that can be obtained by combining work of J.\u00a0Arregi and A.\u00a0Vera-L\u00f3pez and of the authors, but the proof of the theorem in this paper is much more natural.\n                  <\/p>","DOI":"10.1090\/s0025-5718-05-01705-9","type":"journal-article","created":{"date-parts":[[2005,8,10]],"date-time":"2005-08-10T10:23:21Z","timestamp":1123669401000},"page":"2027-2033","source":"Crossref","is-referenced-by-count":11,"title":["Involutions and characters of upper triangular matrix groups"],"prefix":"10.1090","volume":"74","author":[{"given":"I.","family":"Isaacs","sequence":"first","affiliation":[]},{"given":"Dikran","family":"Karagueuzian","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2005,3,24]]},"reference":[{"key":"1","volume-title":"Computational algebra and number theory","year":"1997","issn-type":"print","ISSN":"https:\/\/id.crossref.org\/issn\/0747-7171"},{"key":"2","isbn-type":"print","volume-title":"$\\Bbb{ATLAS}$ of finite groups","author":"Conway, J. H.","year":"1985","ISBN":"https:\/\/id.crossref.org\/isbn\/0198531990"},{"key":"3","series-title":"Wiley Classics Library","isbn-type":"print","volume-title":"Methods of representation theory. Vol. I","author":"Curtis, Charles W.","year":"1990","ISBN":"https:\/\/id.crossref.org\/isbn\/0471523674"},{"key":"4","unstructured":"Isaacs, I. M., Character Theory of Finite Groups, Dover (1994)."},{"issue":"2","key":"5","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"},{"issue":"2","key":"6","doi-asserted-by":"publisher","first-page":"722","DOI":"10.1006\/jabr.1998.7430","article-title":"Erratum: \u201cConjugacy in groups of upper triangular matrices\u201d [J. Algebra 202 (1998), no. 2, 704\u2013711; MR1617655 (99b:20011)]","volume":"208","author":"Isaacs, I. M.","year":"1998","journal-title":"J. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0021-8693","issn-type":"print"},{"issue":"1","key":"7","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/S0747-7171(86)80012-8","article-title":"Computing character degrees in \ud835\udc5d-groups","volume":"2","author":"Slattery, Michael C.","year":"1986","journal-title":"J. Symbolic Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0747-7171","issn-type":"print"},{"issue":"1","key":"8","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0021-8693(92)90085-Z","article-title":"Conjugacy classes in Sylow \ud835\udc5d-subgroups of \ud835\udc3a\ud835\udc3f(\ud835\udc5b,\ud835\udc5e)","volume":"152","author":"Vera L\u00f3pez, Antonio","year":"1992","journal-title":"J. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0021-8693","issn-type":"print"},{"key":"9","unstructured":"Vera L\u00f3pez, A. and Arregi, J., private communication."}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2005-74-252\/S0025-5718-05-01705-9\/S0025-5718-05-01705-9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2005-74-252\/S0025-5718-05-01705-9\/S0025-5718-05-01705-9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T14:31:06Z","timestamp":1776781866000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2005-74-252\/S0025-5718-05-01705-9\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,3,24]]},"references-count":9,"journal-issue":{"issue":"252","published-print":{"date-parts":[[2005,10]]}},"alternative-id":["S0025-5718-05-01705-9"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-05-01705-9","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2005,3,24]]}}}