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. / 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. / Committee in charge: Alexander Kleshchev, Chairperson, Mathematics;
Jonathan Brundan, Member, Mathematics;
Boris Botvinnik, Member, Mathematics;
Victor Ostrik, Member, Mathematics;
William Harbaugh, Outside Member, Economics
| Identifer | oai:union.ndltd.org:uoregon.edu/oai:scholarsbank.uoregon.edu:1794/10871 |
| Date | 06 1900 |
| Creators | Nash, David A., 1982- |
| Publisher | University of Oregon |
| Source Sets | University of Oregon |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
| Relation | University of Oregon theses, Dept. of Mathematics, Ph. D., 2010; |
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