A unipotent realization of the chromatic quasisymmetric function
Combinatorics
2024-09-25 v3 Representation Theory
Abstract
This paper realizes of two families of combinatorial symmetric functions via the complex character theory of the finite general linear group : chromatic quasisymmetric functions and vertical strip LLT polynomials. The associated characters are elementary in nature and can be obtained by induction from certain well-behaved characters of the unipotent upper triangular groups . The proof of these results also gives a general Hopf algebraic approach to computing the induction map. Additional results include a connection between the relevant characters and Hessenberg varieties and a re-interpretation of known theorems and conjectures about the relevant symmetric functions in terms of .
Keywords
Cite
@article{arxiv.2211.06981,
title = {A unipotent realization of the chromatic quasisymmetric function},
author = {Lucas Gagnon},
journal= {arXiv preprint arXiv:2211.06981},
year = {2024}
}