Tilting modules for Lie superalgebras

2002/09/18 by Jonathan Brundan
Mathematics · #math.RT #msc:17B10

paper · pdf

published as Commun. in Algebra 32 (2004), 2251-2268. · 16 pages

arxiv created 2002/09/18 · arxiv updated 2009/11/30

Abstract

This is a companion article to my papers on Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebras gl(m|n) (much revised!) and q(n). The goal is to develop the general theory of tilting modules for Lie superalgebras, working in a general graded setting very similar to work of Soergel (Character formulae for tilting modules over Kac-Moody algebras, Represent. Theory 2 (1998), 432-438) in the Lie algebra case. Examples are given involving the Lie superalgebras gl(m|n) and q(n), but maybe this will also be useful for the other classical and affine Lie superalgebras.

Related

• Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebra gl(m|n)
• The Category O for Lie algebras of vector fields (I): Tilting modules and character formulas
• Representations of a class of infinite-dimensional primitive Lie superalgebras
• Characters and composition factor multiplicities for the Lie superalgebra gl(m/n)
• Lie Superalgebras and Generalized Kazhdan-Lusztig Polynomials