Computing the Lusztig-Vogan bijection

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2017

Author dc:creator

• Rush, David B., Ph. D. Massachusetts Institute of Technology

Advisor dc:contributor.advisor

• David A. Vogan Jr.

• Mathematics.

Statement dc:rights

• 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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/113549

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/113549