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arXiv · 2111.15161

Towards combinatorial invariance for Kazhdan-Lusztig polynomials

Charles Blundell·Lars Buesing·Alex Davies·Petar Veličković·Geordie Williamson
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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.

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Charles Blundell, Lars Buesing, Alex Davies, Petar Veličković, Geordie Williamson. 2021-11-30. Towards combinatorial invariance for Kazhdan-Lusztig polynomials. https://doi.org/10.1090/ert%2F624

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