Séminaire Lotharingien de Combinatoire, 89B.72 (2023), 12 pp.
Lucas Gagnon
A Unipotent Realization of the Chromatic Quasisymmetric Function
Abstract.
The chromatic quasisymmetric function is a t-analogue of Stanley's chromatic symmetric function, and has recently been at the center of a number of exciting developments in algebraic combinatorics.
This extended abstract contributes to this trend, describing a novel realization of certain chromatic quasisymmetric functions as characters of the finite general linear group GLn(Fq).
Additional results tie these characters to other aspects of the chromatic quasisymmetric function: point counting in Hessenberg varieties over Fq, realizing the plethystic connection with unicellular LLT polynomials, and re-interpreting positivity conjectures.
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
The following versions are available: