English

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

Combinatorics 2012-02-20 v2 Representation Theory

Abstract

A combinatorial description of the crystal B()\mathcal{B}(\infty) 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()\mathcal{B}(\infty) 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.

Keywords

Cite

@article{arxiv.1106.0535,
  title  = {A combinatorial description of the Gindikin-Karpelevich formula in type A},
  author = {Kyu-Hwan Lee and Ben Salisbury},
  journal= {arXiv preprint arXiv:1106.0535},
  year   = {2012}
}

Comments

17 pages. Edited using comments from referees