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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Classical groups, integrals and Virasoro constraints

Xu, Da 01 May 2010 (has links)
First, we consider the group integrals where integrands are the monomials of matrix elements of irreducible representations of classical groups. These group integrals are invariants under the group action. Based on analysis on Young tableaux, we investigate some related duality theorems and compute the asymptotics of the group integrals for fixed signatures, as the rank of the classical groups go to infinity. We also obtain the Viraosoro constraints for some partition functions, which are power series of the group integrals. Second, we show that the proof of Witten's conjecture can be simplified by using the fermion-boson correspondence, i.e., the KdV hierarchy and Virasoro constraints of the partition function in Witten's conjecture can be achieved naturally. Third, we consider the partition function involving the invariants that are intersection numbers of the moduli spaces of holomorphic maps in nonlinear sigma model. We compute the commutator of the representation of Virasoro algebra and give a fat graph(ribbon graph) interpretation for each term in the diferential operators.
2

Graded representation theory of Hecke algebras

Nash, David A., 1982- 06 1900 (has links)
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
3

Family Algebras of Representations with Simple Spectrum

rojkovsk@math.upenn.edu 18 June 2001 (has links)
No description available.

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