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

Kyu Hwan Lee; Ben Salisbury

doi:10.1016/j.jcta.2012.01.011

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

Kyu Hwan Lee, Ben Salisbury

Mathematics

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11 Scopus citations

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	https://doi.org/10.1016/j.jcta.2012.01.011
State	Published - Jul 2012

Keywords

Crystals
Gindikin-Karpelevich
MV polytopes
Quiver varieties
Young tableaux

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10.1016/j.jcta.2012.01.011

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title = "A combinatorial description of the Gindikin-Karpelevich formula in type A",

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.",

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AB - 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.

KW - Crystals

KW - Gindikin-Karpelevich

KW - MV polytopes

KW - Quiver varieties

KW - Young tableaux

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SP - 1081

EP - 1094

JO - Journal of Combinatorial Theory, Series A

JF - Journal of Combinatorial Theory, Series A

SN - 0097-3165

IS - 5

ER -

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

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