{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T23:36:22Z","timestamp":1776728182356,"version":"3.51.2"},"reference-count":8,"publisher":"American Mathematical Society (AMS)","issue":"235","license":[{"start":{"date-parts":[[2001,3,14]],"date-time":"2001-03-14T00:00:00Z","timestamp":984528000000},"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":"

\n The Lusztig Conjecture expresses the character of a finite-dimensional irreducible representation of a reductive algebraic group\n \n \n \n G<\/mml:mi>\n G<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n in prime characteristic as a linear combination of characters of Weyl modules for\n \n \n \n G<\/mml:mi>\n G<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n . The representations described by the conjecture are in one-to-one correspondence with the (finitely many) alcoves in the intersection of the dominant cone and the so-called Jantzen region. Each alcove has a length, defined to be the number of alcove walls (hyperplanes) separating it from the fundamental alcove (the unique alcove in the dominant cone whose closure contains the origin). This article determines the maximum length of an alcove in the intersection of the dominant cone with the Jantzen region.\n <\/p>","DOI":"10.1090\/s0025-5718-00-01220-5","type":"journal-article","created":{"date-parts":[[2002,11,6]],"date-time":"2002-11-06T14:02:22Z","timestamp":1036591342000},"page":"1265-1280","source":"Crossref","is-referenced-by-count":1,"title":["Geometry of the Jantzen region in Lusztig\u2019s conjecture"],"prefix":"10.1090","volume":"70","author":[{"given":"Brian","family":"Boe","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2000,3,14]]},"reference":[{"key":"1","doi-asserted-by":"publisher","first-page":"771","DOI":"10.2307\/2371335","article-title":"Infinite number fields with Noether ideal theories","volume":"61","author":"MacLane, Saunders","year":"1939","journal-title":"Amer. J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9327","issn-type":"print"},{"key":"2","series-title":"Actualit\\'{e}s Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1337","volume-title":"\\'{E}l\\'{e}ments de math\\'{e}matique. Fasc. XXXIV. Groupes et alg\\`ebres de Lie. Chapitre IV: Groupes de Coxeter et syst\\`emes de Tits. Chapitre V: Groupes engendr\\'{e}s par des r\\'{e}flexions. Chapitre VI: syst\\`emes de racines","author":"Bourbaki, N.","year":"1968"},{"key":"3","series-title":"Cambridge Studies in Advanced Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511623646","volume-title":"Reflection groups and Coxeter groups","volume":"29","author":"Humphreys, James E.","year":"1990","ISBN":"https:\/\/id.crossref.org\/isbn\/052137510X"},{"key":"4","series-title":"Pure and Applied Mathematics","isbn-type":"print","volume-title":"Representations of algebraic groups","volume":"131","author":"Jantzen, Jens Carsten","year":"1987","ISBN":"https:\/\/id.crossref.org\/isbn\/0123802458"},{"issue":"2","key":"5","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1016\/0001-8708(80)90031-6","article-title":"Hecke algebras and Jantzen\u2019s generic decomposition patterns","volume":"37","author":"Lusztig, George","year":"1980","journal-title":"Adv. in Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0001-8708","issn-type":"print"},{"key":"6","isbn-type":"print","first-page":"313","article-title":"Some problems in the representation theory of finite Chevalley groups","author":"Lusztig, George","year":"1980","ISBN":"https:\/\/id.crossref.org\/isbn\/0821814400"},{"key":"7","unstructured":"M. Sch\u00f6nert et. al., GAP \u2014 Groups, Algorithms, and Programming, Lehrstuhl D f\u00fcr Mathematik, Rheinisch Westf\u00e4lische Technische Hochschule, Aachen, Germany, fifth edition, 1995."},{"issue":"237","key":"8","first-page":"Exp. No. 793, 3, 75--85","article-title":"Conjectures de Lusztig","author":"Soergel, Wolfgang","year":"1996","journal-title":"Ast\\'{e}risque","ISSN":"https:\/\/id.crossref.org\/issn\/0303-1179","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2001-70-235\/S0025-5718-00-01220-5\/S0025-5718-00-01220-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2001-70-235\/S0025-5718-00-01220-5\/S0025-5718-00-01220-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T22:42:09Z","timestamp":1776724929000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2001-70-235\/S0025-5718-00-01220-5\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,3,14]]},"references-count":8,"journal-issue":{"issue":"235","published-print":{"date-parts":[[2001,7]]}},"alternative-id":["S0025-5718-00-01220-5"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-00-01220-5","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":[[2000,3,14]]}}}