Parabolic recursions for Kazhdan-Lusztig polynomials and the hypercube decomposition

Autor:	Gurevich, Maxim, Wang, Chuijia
Rok vydání:	2023
Předmět:	Mathematics - Representation Theory Mathematics - Combinatorics
Druh dokumentu:	Working Paper
Popis:	We employ general parabolic recursion methods to demonstrate the recently devised hypercube formula for Kazhdan-Lusztig polynomials of $S_n$, and establish its generalization to the full setting of a finite Coxeter system through algebraic proof. We introduce procedures for positive decompositions of $q$-derived Kazhdan-Lusztig polynomials within this setting, that utilize classical Hecke algebra positivity phenomena of Dyer-Lehrer and Grojnowski-Haiman. This leads to a distinct algorithmic approach to the subject, based on induction from a parabolic subgroup. We propose suitable weak variants of the combinatorial invariance conjecture and verify their validity for permutation groups. Comment: 23 pages, comments welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2303.09251 Zobrazit plný text záznamu View this record from Arxiv