A Kazhdan-Lusztig Algorithm for Whittaker Modules

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Publication Type dissertation
School or College College of Science
Department Doctor of Philosophy
Author Romanov, Anna
Title A Kazhdan-Lusztig Algorithm for Whittaker Modules
Date 2018
Description This dissertation develops the structure theory of the category Whittaker modules for a complex semisimple Lie algebra. We establish a character theory that distinguishes isomorphism classes of Whittaker modules in the Grothendieck group of the category, then use the localization functor of Beilinson and Bernstein to realize Whittaker modules geometrically as certain twisted D-modules on the associated flag variety (so called "twisted Harish-Chandra sheaves"). The main result of this document is an algorithm for computing the multiplicities of irreducible Whittaker modules in the composition series of standard Whittaker modules, which are generalizations of Verma modules. This algorithm establishes that the multiplicities are determined by a collection of polynomials we refer to as Whittaker Kazhdan--Lusztig polynomials.
Type Text
Publisher University of Utah
Subject Mathematics; Polynomials
Dissertation Name Doctor of Philosophy
Language eng
Rights Management (c) Anna Romanov
Format Medium application/pdf
ARK ark:/87278/s6wb08gm
Setname ir_etd
Date Created 2019-12-09
Date Modified 2019-12-11
ID 1496391
Reference URL https://collections.lib.utah.edu/ark:/87278/s6wb08gm
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