On combinatorial invariance of parabolic Kazhdan-Lusztig polynomials

2024/04/05 by Barkley, Grant T., Gaetz, Christian · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2404.04246

Abstract

We show that the Combinatorial Invariance Conjecture for Kazhdan-Lusztig polynomials due to Lusztig and to Dyer, its parabolic analog due to Marietti, and a refined parabolic version that we introduce, are equivalent. We use this to give a new proof of Marietti's conjecture in the case of lower Bruhat intervals and to prove several new cases of the parabolic conjectures.

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• Intersection cohomology without spaces

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