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Funktsional. Anal. i Prilozhen., 2015, Volume 49, Issue 1, Pages 18–30 (Mi faa3173)  

This article is cited in 1 scientific paper (total in 1 paper)

Characters of the Feigin–Stoyanovsky Subspaces and Brion's Theorem

I. Yu. Makhlin


Abstract: We give an alternative proof of the main result of [B. Feigin, M. Jimbo, S. Loktev, T. Miwa, E. Mukhin, The Ramanujan J., 7:3 (2003), 519–530]; 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 vectors comprising a monomial basis of the subspace and then compute the character by using (a variation of) Brion's theorem.

Keywords: representation theory, affine Lie algebras, character formulas, convex polyhedra, Brion's theorem

DOI: https://doi.org/10.4213/faa3173

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English version:
Functional Analysis and Its Applications, 2015, 49:1, 15–24

Bibliographic databases:

UDC: 512.554.32
Received: 24.02.2014

Citation: I. Yu. Makhlin, “Characters of the Feigin–Stoyanovsky Subspaces and Brion's Theorem”, Funktsional. Anal. i Prilozhen., 49:1 (2015), 18–30; Funct. Anal. Appl., 49:1 (2015), 15–24

Citation in format AMSBIB
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\jour Funktsional. Anal. i Prilozhen.
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\pages 18--30
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Feigin B., Makhlin I., “A combinatorial formula for affine Hall–Littlewood functions via a weighted Brion theorem”, Sel. Math.-New Ser., 22:3 (2016), 1703–1747  crossref  mathscinet  zmath  isi  elib  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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