Crystal graphs, Tokuyama's theorem, and the Gindikin--Karpelevic formula for G_2
Holley Friedlander, Louis Gaudet, Paul E. Gunnells
TL;DR
This paper proposes a conjecture deforming the Weyl character formula for G_2, and proves a combinatorial version of the Gindikin--Karpelevic formula for G_2, extending known results from type A.
Contribution
It introduces a new conjecture for G_2's Weyl character formula and proves a combinatorial Gindikin--Karpelevic formula for this exceptional Lie type.
Findings
Conjectured a deformation of the Weyl character formula for G_2.
Proved a combinatorial Gindikin--Karpelevic formula for G_2.
Extended combinatorial formulas from type A to G_2.
Abstract
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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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Advanced Combinatorial Mathematics