Young tableaux, canonical bases and the Gindikin-Karpelevich formula
Kyu-Hwan Lee, Ben Salisbury
TL;DR
This paper connects Young tableaux with canonical bases and provides a combinatorial formula for the Gindikin-Karpelevich integral, enhancing understanding of Lie algebra representations.
Contribution
It establishes an explicit bijection between Young tableaux and canonical bases, and derives a combinatorial rule for the Gindikin-Karpelevich formula.
Findings
Explicit bijection between Young tableaux and canonical bases
Combinatorial rule for Gindikin-Karpelevich formula
Enhanced combinatorial understanding of Lie algebra representations
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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