Towards combinatorial invariance for Kazhdan-Lusztig polynomials

Blundell, Charles; Buesing, Lars; Davies, Alex; Veličković, Petar; Williamson, Geordie

doi:10.1090/ert/624

Towards combinatorial invariance for Kazhdan-Lusztig polynomials
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by Charles Blundell, Lars Buesing, Alex Davies, Petar Veličković and Geordie Williamson

Represent. Theory 26 (2022), 1145-1191

DOI: https://doi.org/10.1090/ert/624

Published electronically: November 16, 2022

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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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