Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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YOUNG TABLEAUX, CANONICAL BASES, AND THE GINDIKIN-KARPELEVICH FORMULA

  • Lee, Kyu-Hwan (Department of Mathematics University of Connecticut) ;
  • Salisbury, Ben (Department of Mathematics The City College of New York, The Institute for Computational and Experimental Research in Mathematics Brown University)
  • Received : 2013.04.09
  • Published : 2014.03.01
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Abstract

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 Gindikin-Karpelevich formula as a sum over the set of Young tableaux.

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References

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