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

I. Yu Makhlin

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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 (Formula presented.). 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.

Original languageEnglish
Pages (from-to)15-24
Number of pages10
JournalFunctional Analysis and its Applications
Issue number1
Publication statusPublished - 2015
Externally publishedYes


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


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