Browsing Mathematics Theses and Dissertations by Author "Nash, David A., 1982"
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Nash, David A., 1982 (University of Oregon, June , 2010)[more][less]Nash, David A., 1982 20101203T22:54:08Z 20101203T22:54:08Z 201006 http://hdl.handle.net/1794/10871 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 IwahoriHecke 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 LascouxLeclercThibon 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 twocolumn 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 en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2010; Symmetric groups Specht modules Irreducible representation Graded representation Hecke algebras Mathematics Theoretical mathematics Graded representation theory of Hecke algebras Thesis
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