On combinatorial invariance of parabolic Kazhdan-Lusztig polynomials

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.

v3: final version, to appear in Selecta Mathematica

References in corpus (3)

• Towards combinatorial invariance for Kazhdan-Lusztig polynomials
• Combinatorial invariance for Kazhdan-Lusztig $R$-polynomials of elementary intervals
• Special idempotents and projections

Cited by in corpus (1)

• The BBDVW Conjecture for Kazhdan-Lusztig polynomials of lower intervals