Graded representation theory of Hecke algebras
by Nash, David A., Ph.D., UNIVERSITY OF OREGON, 2010, 76 pages; 3420425

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 pth-root of unity to those of the group algebra of the symmetric group over a field of characteristic p.

 
AdviserAlexander S. Kleshchev
SchoolUNIVERSITY OF OREGON
SourceDAI/B 71-09, p. , Sep 2010
Source TypeDissertation
SubjectsMathematics; Theoretical mathematics
Publication Number3420425
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