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.
|Commitee:||Hecht, Henryk, Ondrus, Matt, Savin, Gordan, Treibergs, Andrejs|
|School:||The University of Utah|
|School Location:||United States -- Utah|
|Source:||DAI-B 72/10, Dissertation Abstracts International|
|Keywords:||Associated cycles, Harish-Chandra modules, Indefinite unitary groups|
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