Crystal graphs, Tokuyama's theorem, and the Gindikin-Karpelevič formula for \(G_{2}\)

DOI10.1007/s10801-014-0567-9zbMath1316.05128arXiv1402.0411OpenAlexW2072532945MaRDI QIDQ2354056

Louis Gaudet, Holley Friedlander, Paul E. Gunnells

Publication date: 10 July 2015

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.0411

zbMATH Keywords

Whittaker functionscharacter formulascrystal graphsLittelmann patternsGindikin-Karpelevič formula

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Ordinary representations and characters (20C15) Dirichlet series in several complex variables associated to automorphic forms; Weyl group multiple Dirichlet series (11F68) Combinatorial aspects of groups and algebras (05E16)

Related Items (3)

Resonant Mirković-Vilonen polytopes and formulas for highest-weight characters ⋮ The flush statistic on semistandard Young tableaux ⋮ On a conjecture about an analogue of Tokuyama's theorem for \(G_2\)

Cites Work

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• Quantum affine algebras, canonical bases, and \(q\)-deformation of arithmetical functions
• Representation theory of \(p\)-adic groups and canonical bases
• Metaplectic Whittaker functions and crystal bases
• The generating function of strict Gelfand patterns and some formulas on characters of general linear groups
• Cones, crystals, and patterns
• Crystals via the affine Grassmannian
• Symplectic shifted tableaux and deformations of Weyl's denominator formula for \(\text{sp}(2n)\)
• Weyl Group Multiple Dirichlet Series
• Integration on $p$-adic groups and crystal bases
• Introduction: Multiple Dirichlet Series
• Metaplectic Whittaker Functions and Crystals of Type B
• Littelmann Patterns and Weyl Group Multiple Dirichlet Series of Type D

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