Kazhdan-Lusztig polynomials and subexpressions

2020/03/31 by Libedinsky, Nicolas, Williamson, Geordie
#05E10 #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2004.00045

Abstract

We refine an idea of Deodhar, whose goal is a counting formula for Kazhdan-Lusztig polynomials. This is a consequence of a simple observation that one can use the solution of Soergel's conjecture to make ambiguities involved in defining certain morphisms between Soergel bimodules in characteristic zero (double leaves) disappear.

Related

• Soergel bimodules and Kazhdan-Lusztig polynomials
• Leading coefficients of Kazhdan--Lusztig polynomials for Deodhar elements
• A Generalization of Deodhar's Framework for Questions in Kazhdan-Lusztig\n Theory
• Embedded factor patterns for Deodhar elements in Kazhdan-Lusztig theory
• Light leaves and Lusztig's conjecture