Young tableaux, canonical bases, and the Gindikin-Karpelevich formula

Kyu Hwan Lee; Ben Salisbury

doi:10.4134/JKMS.2014.51.2.289

Young tableaux, canonical bases, and the Gindikin-Karpelevich formula

Kyu Hwan Lee, Ben Salisbury

Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

A combinatorial description of the crystal B(∞) for finitedimensional simple Lie algebras in terms of certain Young tableaux was developed by J. Hong and H. Lee. We establish an explicit bijection between these Young tableaux and canonical bases indexed by Lusztig's parametrization, and obtain a combinatorial rule for expressing the Gindikin-Karpelevich formula as a sum over the set of Young tableaux.

Original language	English
Pages (from-to)	289-309
Number of pages	21
Journal	Journal of the Korean Mathematical Society
Volume	51
Issue number	2
DOIs	https://doi.org/10.4134/JKMS.2014.51.2.289
State	Published - 2014

Keywords

Canonical basis
Crystal
Gindikin-karpelevich
Kostant partition
Lusztig parametrization
Young tableaux

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10.4134/JKMS.2014.51.2.289

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abstract = "A combinatorial description of the crystal B(∞) for finitedimensional simple Lie algebras in terms of certain Young tableaux was developed by J. Hong and H. Lee. We establish an explicit bijection between these Young tableaux and canonical bases indexed by Lusztig's parametrization, and obtain a combinatorial rule for expressing the Gindikin-Karpelevich formula as a sum over the set of Young tableaux.",

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AU - Salisbury, Ben

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AB - A combinatorial description of the crystal B(∞) for finitedimensional simple Lie algebras in terms of certain Young tableaux was developed by J. Hong and H. Lee. We establish an explicit bijection between these Young tableaux and canonical bases indexed by Lusztig's parametrization, and obtain a combinatorial rule for expressing the Gindikin-Karpelevich formula as a sum over the set of Young tableaux.

KW - Canonical basis

KW - Crystal

KW - Gindikin-karpelevich

KW - Kostant partition

KW - Lusztig parametrization

KW - Young tableaux

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JO - Journal of the Korean Mathematical Society

JF - Journal of the Korean Mathematical Society

IS - 2

ER -

Young tableaux, canonical bases, and the Gindikin-Karpelevich formula

Abstract

Keywords

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