Work

Parabolic recursions for Kazhdan–Lusztig polynomials and the hypercube decomposition

Year: 2024

Type: article

Abstract: We employ general parabolic recursion methods to demonstrate the recently devised hypercube formula for Kazhdan-Lusztig polynomials of $$S_n$$ 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.

Source: Selecta Mathematica

DOI: 10.1007/s00029-024-00972-0

Authors: Maxim Gurevich, Chuijia Wang

Institutions: Technion – Israel Institute of Technology, Chinese University of Hong Kong

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: Technion-Israel Institute of Technology