{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T11:13:44Z","timestamp":1758280424872},"reference-count":36,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2009,6]]},"abstract":"<jats:p> We describe irreducible representations and character formulas of the Renner monoids for reductive monoids, which generalize the Munn\u2013Solomon representation theory of rook monoids to any Renner monoids. The type map and polytope associated with reductive monoids play a crucial role in our work. It turns out that the irreducible representations of certain parabolic subgroups of the Weyl groups determine the complete set of irreducible representations of the Renner monoids. An analogue of the Munn\u2013Solomon formula for calculating the character of the Renner monoids, in terms of the characters of the parabolic subgroups, is shown. <\/jats:p>","DOI":"10.1142\/s0218196709005147","type":"journal-article","created":{"date-parts":[[2009,6,16]],"date-time":"2009-06-16T21:30:55Z","timestamp":1245187855000},"page":"511-525","source":"Crossref","is-referenced-by-count":5,"title":["REPRESENTATIONS OF THE RENNER MONOID"],"prefix":"10.1142","volume":"19","author":[{"given":"ZHUO","family":"LI","sequence":"first","affiliation":[{"name":"Department of Mathematics, Xiangtan University, Xiangtan, Hunan 411105, P. R. China"}]},{"given":"ZHENHENG","family":"LI","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, University of South Carolina Aiken, Aiken, SC 29801, USA"}]},{"given":"YOU'AN","family":"CAO","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Xiangtan University, Xiangtan, Hunan 411105, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/007.1"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-0019-9"},{"key":"rf3","volume-title":"Basic Algebra II","author":"Jacobson N.","year":"1980"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196708004640"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2005.12.008"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196703001304"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100029868"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100031935"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100031947"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1991-1020044-8"},{"key":"rf11","first-page":"241","volume":"38","author":"Ponizovskii I.","journal-title":"Mat. Sb. N.S."},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1155\/S0161171281000513"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511600661"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1993-1127157-2"},{"key":"rf15","first-page":"623","volume":"73","author":"Putcha M.","journal-title":"Proc. London Math. Soc."},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-97-01823-0"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1997.7395"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2004.03.001"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1023\/B:JACO.0000047291.42015.a6"},{"key":"rf20","author":"Putcha M.","journal-title":"J. Algebraic Combin."},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2004.03.001"},{"key":"rf22","first-page":"385","volume":"226","author":"Putcha M.","journal-title":"J. Algebra"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1993-1091231-X"},{"key":"rf24","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(86)90197-3"},{"key":"rf25","unstructured":"L.\u00a0Renner, Semigroups, Formal Language and Groups, ed. J.\u00a0Fountain (Kluwer Academic Publishers, 1995)\u00a0pp. 31\u201339."},{"key":"rf26","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(98)00163-7"},{"key":"rf27","series-title":"Series: Encyclopedia of Mathematical Sciences","volume-title":"Linear Algebraic Monoids","volume":"134","author":"Renner L.","year":"2005"},{"key":"rf28","doi-asserted-by":"publisher","DOI":"10.1007\/s10801-008-0141-4"},{"key":"rf29","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9800(67)80064-4"},{"key":"rf30","first-page":"15","volume":"36","author":"Solomon L.","journal-title":"Geom. Dedicata"},{"key":"rf31","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-8693(02)00004-2"},{"key":"rf32","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-0149-3_10"},{"key":"rf33","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511805967"},{"key":"rf34","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2005.08.004"},{"key":"rf35","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2007.12.001"},{"key":"rf36","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8431-1"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196709005147","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:19:06Z","timestamp":1565115546000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196709005147"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,6]]},"references-count":36,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2009,6]]}},"alternative-id":["10.1142\/S0218196709005147"],"URL":"https:\/\/doi.org\/10.1142\/s0218196709005147","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,6]]}}}