A Combinatorial Formula for Affine Hall-Littlewood Functions via a Weighted Brion Theorem
Combinatorics
2016-07-12 v4 Representation Theory
Abstract
We present a new combinatorial formula for Hall-Littlewood functions associated with the affine root system of type , i.e. corresponding to the affine Lie algebra . Our formula has the form of a sum over the elements of a basis constructed by Feigin, Jimbo, Loktev, Miwa and Mukhin in the corresponding irreducible representation. Our formula can be viewed as a weighted sum of exponentials of integer points in a certain infinite-dimensional convex polyhedron. We derive a weighted version of Brion's theorem and then apply it to our polyhedron to prove the formula.
Keywords
Cite
@article{arxiv.1505.04269,
title = {A Combinatorial Formula for Affine Hall-Littlewood Functions via a Weighted Brion Theorem},
author = {Boris Feigin and Igor Makhlin},
journal= {arXiv preprint arXiv:1505.04269},
year = {2016}
}