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 GL_n(F_q). Additional results tie these characters to other aspects of the chromatic quasisymmetric function: point counting in Hessenberg varieties over F_q, 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.

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