dc.contributor.author |
Nash, David A., 1982- |
|
dc.date.accessioned |
2010-12-03T22:54:08Z |
|
dc.date.available |
2010-12-03T22:54:08Z |
|
dc.date.issued |
2010-06 |
|
dc.identifier.uri |
http://hdl.handle.net/1794/10871 |
|
dc.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. |
en_US |
dc.description.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. |
en_US |
dc.description.sponsorship |
Committee in charge: Alexander Kleshchev, Chairperson, Mathematics;
Jonathan Brundan, Member, Mathematics;
Boris Botvinnik, Member, Mathematics;
Victor Ostrik, Member, Mathematics;
William Harbaugh, Outside Member, Economics |
en_US |
dc.language.iso |
en_US |
en_US |
dc.publisher |
University of Oregon |
en_US |
dc.relation.ispartofseries |
University of Oregon theses, Dept. of Mathematics, Ph. D., 2010; |
|
dc.subject |
Symmetric groups |
en_US |
dc.subject |
Specht modules |
en_US |
dc.subject |
Irreducible representation |
en_US |
dc.subject |
Graded representation |
en_US |
dc.subject |
Hecke algebras |
en_US |
dc.subject |
Mathematics |
en_US |
dc.subject |
Theoretical mathematics |
en_US |
dc.title |
Graded representation theory of Hecke algebras |
en_US |
dc.type |
Thesis |
en_US |