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Computing the Lusztig-Vogan bijection

Author(s)
Rush, David B., Ph. D. Massachusetts Institute of Technology
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Massachusetts Institute of Technology. Department of Mathematics.
Advisor
David A. Vogan Jr.
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MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission. http://dspace.mit.edu/handle/1721.1/7582
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Abstract
Let G be a connected complex reductive algebraic group with Lie algebra g. The Lusztig-Vogan bijection relates two bases for the bounded derived category of G-equivariant coherent sheaves on the nilpotent cone 11 of g. One basis is indexed by ..., the set of dominant weights of G, and the other by [Omega], the set of pairs ... consisting of a nilpotent orbit ... and an irreducible G-equivariant vector bundle ... The existence of the Lusztig-Vogan bijection ... was proven by Bezrukavnikov, and an algorithm computing [gamma] in type A was given by Achar. Herein we present a combinatorial description of [gamma] in type A that subsumes and dramatically simplifies Achar's algorithm.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2017.
 
Cataloged from PDF version of thesis.
 
Includes bibliographical references (pages 129-130).
 
Date issued
2017
URI
http://hdl.handle.net/1721.1/113549
Department
Massachusetts Institute of Technology. Department of Mathematics
Publisher
Massachusetts Institute of Technology
Keywords
Mathematics.

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