Functional Analysis and Its Applications

, Volume 49, Issue 1, pp 15–24 | Cite as

Characters of the Feigin-Stoyanovsky subspaces and Brion’s theorem

  • I. Yu. Makhlin


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.

Key words

representation theory affine Lie algebras character formulas convex polyhedra Brion’s theorem 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.International Laboratory of Representation Theory and Mathematical PhysicsNational Research University “Higher School of Economics”MoscowRussia

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