Computing the Lusztig-Vogan bijection
Author(s)
Rush, David B., Ph. D. Massachusetts Institute of Technology
DownloadFull printable version (5.670Mb)
Other Contributors
Massachusetts Institute of Technology. Department of Mathematics.
Advisor
David A. Vogan Jr.
Terms of use
Metadata
Show full item recordAbstract
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
2017Department
Massachusetts Institute of Technology. Department of MathematicsPublisher
Massachusetts Institute of Technology
Keywords
Mathematics.