Brion’s theorem for Gelfand–Tsetlin polytopes

I. Yu Makhlin

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


This work is motivated by the observation that the character of an irreducible gln-module (a Schur polynomial), being the sum of exponentials of integer points in a Gelfand–Tsetlin polytope, can be expressed by using Brion’s theorem. The main result is that, in the case of a regular highest weight, the contributions of all nonsimplicial vertices vanish, while the number of simplicial vertices is n! and the contributions of these vertices are precisely the summands in Weyl’s character formula.

Original languageEnglish
Pages (from-to)98-106
Number of pages9
JournalFunctional Analysis and its Applications
Issue number2
Publication statusPublished - 1 Apr 2016
Externally publishedYes


  • Brion’s theorem
  • Gelfand–Tsetlin polytopes
  • general linear Lie algebra
  • Schur polynomials


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