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Title of Journal: Sel Math New Ser

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Abbravation: Selecta Mathematica

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Springer International Publishing

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DOI

10.1016/0172-2190(86)90188-2

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1420-9020

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A combinatorial formula for affine Hall–Littlewood

Authors: Boris Feigin Igor Makhlin
Publish Date: 2016/03/19
Volume: 22, Issue: 3, Pages: 1703-1747
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Abstract

We present a new combinatorial formula for Hall–Littlewood functions associated with the affine root system of type tildeA n1 ie corresponding to the affine Lie algebra widehatmathfrak 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 infinitedimensional convex polyhedron We derive a weighted version of Brion’s theorem and then apply it to our polyhedron to prove the formula

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