Equivalence between invariance conjectures for parabolic Kazhdan-Lusztig polynomials

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. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.