Towards combinatorial invariance for Kazhdan-Lusztig polynomials

Abstract

Kazhdan-Lusztig polynomials are important and mysterious objects in representation theory. Here we present a new formula for their computation for symmetric groups based on the Bruhat graph. Our approach suggests a solution to the combinatorial invariance conjecture for symmetric groups, a well-known conjecture formulated by Lusztig and Dyer in the 1980s.

47 pages, comments welcome

References in corpus (3)

• Governing Singularities of Schubert Varieties
• An overview of Morihiko Saito's theory of mixed Hodge modules
• Combinatorial invariance conjecture for ${\tilde{A}}_2$

Cited by in corpus (3)

• Combinatorial invariance for Kazhdan-Lusztig $R$-polynomials of elementary intervals
• On combinatorial invariance of parabolic Kazhdan-Lusztig polynomials
• The BBDVW Conjecture for Kazhdan-Lusztig polynomials of lower intervals