%0 Journal Article
%T Characters of Feigin-Stoyanovsky subspaces and Brion's theorem
%A Igor Makhlin
%J Mathematics
%D 2014
%I arXiv
%X We give an alternative proof of the main result of the paper http://arxiv.org/abs/math/0112104, 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 $\widehat{\mathfrak{sl}_n}(\mathbb{C})$. Our approach is to assign integer points of a certain polytope to the vectors comprising a monomial basis of the subspace and then compute the character via (a variation of) Brion's theorem.
%U http://arxiv.org/abs/1402.5506v1