Equivalence between invariance conjectures for parabolic Kazhdan-Lusztig polynomials

TL;DR

This paper establishes that the combinatorial invariance conjecture for parabolic Kazhdan-Lusztig polynomials is equivalent to its restriction to maximal quotients, linking it to recent results on Kazhdan-Lusztig polynomial invariance.

Contribution

It proves the equivalence between the invariance conjecture for parabolic Kazhdan-Lusztig polynomials and its restriction to maximal quotients, extending understanding of invariance properties.

Findings

Proves the equivalence of invariance conjectures for parabolic Kazhdan-Lusztig polynomials and their maximal quotient restrictions.

Links the invariance conjecture for parabolic Kazhdan-Lusztig polynomials to recent results on Kazhdan-Lusztig polynomial invariance.

Provides a new perspective on the symmetry and invariance properties in the theory of Kazhdan-Lusztig polynomials.

Abstract

We prove that the combinatorial invariance conjecture for parabolic Kazhdan-Lusztig polynomials, formulated by Mario Marietti, is equivalent to its restriction to maximal quotients. This equivalence lies at the other extreme in respect to the equivalence, recently proved by Barkley and Gaetz, with the invariance conjecture for Kazhdan-Lusztig polynomials, which turns out to be equivalent to the conjecture for maximal quotients.