Abstract
We give an alternative proof of the main result of [1]; the proof relies on Brion’s theorem about convex polyhedra. The result itself can be viewed as a formula for the character of the Feigin-Stoyanovsky subspace of an integrable irreducible representation of the affine Lie algebra \(widehat {s{l_n}}(\mathbb{C})\). Our approach is to assign integer points of a certain polytope to vectors comprising a monomial basis of the subspace and then compute the character by using (a variation of) Brion’s theorem.
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References
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 49, No. 1, pp. 18–30, 2015
Original Russian Text Copyright © by I. Yu. Makhlin
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Makhlin, I.Y. Characters of the Feigin-Stoyanovsky subspaces and Brion’s theorem. Funct Anal Its Appl 49, 15–24 (2015). https://doi.org/10.1007/s10688-015-0079-y
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DOI: https://doi.org/10.1007/s10688-015-0079-y