A combinatorial formula for affine Hall–Littlewood functions via a weighted Brion theorem

Boris Feigin, Igor Makhlin

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We present a new combinatorial formula for Hall–Littlewood functions associated with the affine root system of type A~ n - 1, i.e., corresponding to the affine Lie algebra sl^ n. 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.

Original languageEnglish
Pages (from-to)1703-1747
Number of pages45
JournalSelecta Mathematica, New Series
Volume22
Issue number3
DOIs
Publication statusPublished - 1 Jul 2016
Externally publishedYes

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