Work

Combinatorial Invariance Conjecture for $\widetilde {A}_2$

Year: 2022

Type: article

Abstract: The combinatorial invariance conjecture (due independently to Lusztig and Dyer) predicts that if $[x,y]$ and $[x^{\prime},y^{\prime}]$ are isomorphic Bruhat posets (of possibly different Coxeter systems), then the corresponding Kazhdan–Lusztig polynomials are equal, that is, $P_{x,y}(q)=P_{x^{\prime},y^{\prime}}(q)$. We prove this conjecture for the affine Weyl group of type $\widetilde {A}_2$. This is the first infinite group with non-trivial Kazhdan–Lusztig polynomials where the conjecture is proved.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnac105

Authors: Gaston Burrull, Nicolas Libedinsky, David Plaza

Institutions: The University of Sydney, University of Chile, University of Talca

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Agenția Națională pentru Cercetare și Dezvoltare

Awards: G1609695865, G470341160, G5948629799