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Regular version of the site

Article

Characters of Feigin-Stoyanovsky subspaces and Brion's theorem

Functional Analysis and Its Applications. 2015. Vol. 49. No. 1. P. 15-24.

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 widehatsln(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.