Graded representation theory of Hecke algebras

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dc.contributor.authorNash, David A., 1982-
dc.date.accessioned2010-12-03T22:54:08Z
dc.date.available2010-12-03T22:54:08Z
dc.date.issued2010-06
dc.descriptionxii, 76 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number.en_US
dc.description.abstractWe study the graded representation theory of the Iwahori-Hecke algebra, denoted by Hd , of the symmetric group over a field of characteristic zero at a root of unity. More specifically, we use graded Specht modules to calculate the graded decomposition numbers for Hd . The algorithm arrived at is the Lascoux-Leclerc-Thibon algorithm in disguise. Thus we interpret the algorithm in terms of graded representation theory. We then use the algorithm to compute several examples and to obtain a closed form for the graded decomposition numbers in the case of two-column partitions. In this case, we also precisely describe the 'reduction modulo p' process, which relates the graded irreducible representations of Hd over [Special characters omitted.] at a p th -root of unity to those of the group algebra of the symmetric group over a field of characteristic p.en_US
dc.description.sponsorshipCommittee in charge: Alexander Kleshchev, Chairperson, Mathematics; Jonathan Brundan, Member, Mathematics; Boris Botvinnik, Member, Mathematics; Victor Ostrik, Member, Mathematics; William Harbaugh, Outside Member, Economicsen_US
dc.identifier.urihttps://hdl.handle.net/1794/10871
dc.language.isoen_USen_US
dc.publisherUniversity of Oregonen_US
dc.relation.ispartofseriesUniversity of Oregon theses, Dept. of Mathematics, Ph. D., 2010;
dc.subjectSymmetric groupsen_US
dc.subjectSpecht modulesen_US
dc.subjectIrreducible representationen_US
dc.subjectGraded representationen_US
dc.subjectHecke algebrasen_US
dc.subjectMathematicsen_US
dc.subjectTheoretical mathematicsen_US
dc.titleGraded representation theory of Hecke algebrasen_US
dc.typeThesisen_US

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