Journal of the
Korean Mathematical Society JKMS

A combinatorial description of the crystal $\mathcal{B}(\infty)$ 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.

Keywords: Gindikin-Karpelevich, Kostant partition, Young tableaux, canonical basis, Lusztig parametrization, crystal

MSC numbers: Primary 17B37; Secondary 05E10