Year: 2024
Type: article
Abstract: We realize two families of combinatorial symmetric functions via the complex character theory of the finite general linear group GL n ކ( q ): chromatic quasisymmetric functions and vertical strip LLT polynomials.The associated GL n ކ( q ) characters are elementary in nature and can be obtained by induction from certain well-behaved characters of the unipotent upper triangular groups UT n ކ( q ).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 GL n ކ( q ) characters and Hessenberg varieties and a reinterpretation of known theorems and conjectures about the relevant symmetric functions in terms of GL n ކ( q ).
Source: Algebra & Number Theory
Author: Lucas Gagnon
Institution: University of Colorado Boulder
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Funder: University of Colorado Boulder
OpenAlex ID: W4402647173