Young tableaux, canonical bases and the Gindikin-Karpelevich formula
Representation Theory
2014-03-20 v3 Combinatorics
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.
Keywords
Cite
@article{arxiv.1205.6006,
title = {Young tableaux, canonical bases and the Gindikin-Karpelevich formula},
author = {Kyu-Hwan Lee and Ben Salisbury},
journal= {arXiv preprint arXiv:1205.6006},
year = {2014}
}
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19 pages