Young tableaux, canonical bases, and the Gindikin-Karpelevich formula

Kyu Hwan Lee, Ben Salisbury

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

A combinatorial description of the crystal B(∞) for finitedimensional simple Lie algebras in terms of certain Young tableaux was developed by J. Hong and H. Lee. We establish an explicit bijection between these Young tableaux and canonical bases indexed by Lusztig's parametrization, and obtain a combinatorial rule for expressing the Gindikin-Karpelevich formula as a sum over the set of Young tableaux.

Original languageEnglish
Pages (from-to)289-309
Number of pages21
JournalJournal of the Korean Mathematical Society
Volume51
Issue number2
DOIs
StatePublished - 2014

Keywords

  • Canonical basis
  • Crystal
  • Gindikin-karpelevich
  • Kostant partition
  • Lusztig parametrization
  • Young tableaux

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