A combinatorial description of the Gindikin-Karpelevich formula in type A

Kyu Hwan Lee, Ben Salisbury

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

A combinatorial description of the crystal B(∞) for finite-dimensional simple Lie algebras in terms of Young tableaux was developed by J. Hong and H. Lee. Using this description, we obtain a combinatorial rule for expressing the Gindikin-Karpelevich formula as a sum over B(∞) when the underlying Lie algebra is of type A. We also interpret our description in terms of MV polytopes and irreducible components of quiver varieties.

Original languageEnglish
Pages (from-to)1081-1094
Number of pages14
JournalJournal of Combinatorial Theory, Series A
Volume119
Issue number5
DOIs
StatePublished - Jul 2012

Keywords

  • Crystals
  • Gindikin-Karpelevich
  • MV polytopes
  • Quiver varieties
  • Young tableaux

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