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arXiv · 1205.6006

Young tableaux, canonical bases and the Gindikin-Karpelevich formula

Kyu-Hwan Lee·Ben Salisbury
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Abstract

A combinatorial description of the crystal B(infinity) for finite-dimensional 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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Kyu-Hwan Lee, Ben Salisbury. 2013-04-08. Young tableaux, canonical bases and the Gindikin-Karpelevich formula. https://doi.org/10.4134/jkms.2014.51.2.289

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