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

Abstract

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.

17 pages. Edited using comments from referees

References in corpus (1)

• Metaplectic Whittaker Functions and Crystal Bases

Cited by in corpus (5)

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• Crystal $\Bla$ in $B(\infty )$ for $G_2$ type Lie Algebra
• A combinatorial description of the affine Gindikin-Karpelevich formula of type A_n^(1)