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We conjecture a deformation of the Weyl character formula for type G_2 in thespirit of Tokuyama's formula for type A. Using our conjecture we prove acombinatorial version of the Gindikin--Karpelevic formula for G_2, in thespirit of Bump--Nakasuji's formula for type A.

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