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 language | English |
---|---|
Pages (from-to) | 1081-1094 |
Number of pages | 14 |
Journal | Journal of Combinatorial Theory, Series A |
Volume | 119 |
Issue number | 5 |
DOIs | |
State | Published - Jul 2012 |
Keywords
- Crystals
- Gindikin-Karpelevich
- MV polytopes
- Quiver varieties
- Young tableaux