Towards combinatorial invariance for Kazhdan-Lusztig polynomials
Charles Blundell, Lars Buesing, Alex Davies, Petar Veličković, Geordie Williamson
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.
Direct links to the papers: https://www.nature.com/articles/s41586-021-04086-x "Advancing mathematics by guiding human intuition with AI" https://arxiv.org/abs/2111.15323 "The signature and cusp geometry of hyperbolic knots" https://arxiv.org/abs/2111.15161 "Towards…
https://arxiv.org/abs/2111.15161
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