YOUNG TABLEAUX, CANONICAL BASES, AND THE GINDIKIN-KARPELEVICH FORMULA

다국어 초록 (Multilingual Abstract)

A combinatorial description of the crystal B(∞) 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 Gindi- kin-Karpelevich formula as a sum over the set of Young tableaux.

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