Computing the Lusztig-Vogan bijection
Name
1020252308-MIT.pdf
Description
Full printable version
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5.67 MB
Format
Adobe PDF
Checksum (MD5)
42c00e46038b01e37807467c0058487e
Author(s)
Rush, David B., Ph. D. Massachusetts Institute of Technology
Advisor(s)
David A. Vogan Jr.
Date Issued
2017
Publisher
Massachusetts Institute of Technology
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).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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