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YOUNG TABLEAUX, CANONICAL BASES, AND THE GINDIKIN-KARPELEVICH FORMULA
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 Title & Authors
YOUNG TABLEAUX, CANONICAL BASES, AND THE GINDIKIN-KARPELEVICH FORMULA
Lee, Kyu-Hwan; Salisbury, Ben;
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 Abstract
A combinatorial description of the crystal 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
Gindikin-Karpelevich;Kostant partition;Young tableaux;canonical basis;Lusztig parametrization;crystal;
 Language
English
 Cited by
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Crystal ℬ ( λ ) $\mathcal {B}(\lambda )$ as a Subset of the Tableau Description of ℬ ( ∞ ) $\mathcal {B}(\infty )$ for the Classical Lie Algebra Types, Algebras and Representation Theory, 2015, 18, 1, 137  crossref(new windwow)
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