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

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

2011-06-02

arxiv.org/abs/1106.0535v2

J. Combin. Theory Ser. A. 119 (2012), 1081-1094

Mathematics

Combinatorics

17 pages. Edited using comments from referees

Scientific paper

10.1016/j.jcta.2012.01.011

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

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