Geodesic
Crystal graphs, Tokuyama's theorem, and the Gindikin-Karpelevič formula for $G_{2}$
Journal of Algebraic Combinatorics, Tome 41 (2015) no. 4, pp. 1089-1102.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We conjecture a deformation of the Weyl character formula for type $G_{2}$ in the spirit of Tokuyama's formula for type $A$. Using our conjecture, we prove a combinatorial version of the Gindikin-Karpelevič formula for $G_{2}$, in the spirit of Bump-Nakasuji's formula for type $A$.
Classification : 05E15, 17B10, 11F68, 20C15, 05E10
Keywords: character formulas, Whittaker functions, Gindikin-Karpelevič formula, crystal graphs, Littelmann patterns 
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     author = {Friedlander, Holley and Gaudet, Louis and Gunnells, Paul E.},
     title = {Crystal graphs, {Tokuyama's} theorem, and the {Gindikin-Karpelevi\v{c}} formula for $G_{2}$},
     journal = {Journal of Algebraic Combinatorics},
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     number = {4},
     year = {2015},
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Friedlander, Holley; Gaudet, Louis; Gunnells, Paul E. Crystal graphs, Tokuyama's theorem, and the Gindikin-Karpelevič formula for $G_{2}$. Journal of Algebraic Combinatorics, Tome 41 (2015) no. 4, pp. 1089-1102. http://geodesic.mathdoc.fr/item/JAC_2015__41_4_a3/