Kyu-Hwan Lee, Ben Salisbury
Published 2012-05-27, updated 2013-04-08Version 3
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.
Comments: 19 pages
Journal: J. Korean Math. Soc. 51 (2014), No. 2, pp. 289-309
Positivity vs negativity of canonical bases
A combinatorial description of the affine Gindikin-Karpelevich formula of type A_n^(1)
Weight multiplicities and Young tableaux through affine crystals
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