Graded representation theory of Hecke algebras
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Date
2010-06
Authors
Nash, David A., 1982-
Journal Title
Journal ISSN
Volume Title
Publisher
University of Oregon
Abstract
We 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.
Description
xii, 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.
Keywords
Symmetric groups, Specht modules, Irreducible representation, Graded representation, Hecke algebras, Mathematics, Theoretical mathematics