Crystal graphs, Tokuyama's theorem, and the Gindikin--Karpelevic formula for G_2

Holley Friedlander; Louis Gaudet; Paul E. Gunnells

arxiv: 1402.0411 · v1 · pith:WZ7QTWS3new · submitted 2014-02-03 · 🧮 math.CO · math.NT· math.RT

Crystal graphs, Tokuyama's theorem, and the Gindikin--Karpelevic formula for G₂

Holley Friedlander , Louis Gaudet , Paul E. Gunnells This is my paper

classification 🧮 math.CO math.NTmath.RT

keywords formulatypeconjecturegindikin--karpelevicspirittokuyamabump--nakasujicharacter

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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--Karpelevic formula for G_2, in the spirit of Bump--Nakasuji's formula for type A.

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Crystal graphs, Tokuyama's theorem, and the Gindikin--Karpelevic formula for G₂

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