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Dissertation/Thesis Abstract

Polynomial representations and associated cycles for indefinite unitary groups
by Housley, Matthew, Ph.D., The University of Utah, 2011, 75; 3461625
Abstract (Summary)

The associated variety is a geometric invariant attached to each Harish-Chandra module of a real reductive Lie group. The associated cycle is a finer invariant that gives additional algebraic data for each component of the associated variety. The main result of this thesis is a set of formulas for associated cycles of a large class of Harish-Chandra modules for the real Lie group U(p, q). These formulas give the associated cycle polynomials for the coherent family containing a module X when elements of the dense orbit in the associated variety of X have a single nontrivial Jordan block or exactly two Jordan blocks.

Indexing (document details)
Advisor: Trapa, Peter
Commitee: Hecht, Henryk, Ondrus, Matt, Savin, Gordan, Treibergs, Andrejs
School: The University of Utah
Department: Mathematics
School Location: United States -- Utah
Source: DAI-B 72/10, Dissertation Abstracts International
Subjects: Mathematics
Keywords: Associated cycles, Harish-Chandra modules, Indefinite unitary groups
Publication Number: 3461625
ISBN: 978-1-124-75232-7
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