Metaplectic Whittaker functions and crystal bases

DOI10.1215/00127094-2010-064zbMath1217.22015arXiv0907.2675OpenAlexW2952926919MaRDI QIDQ619690

Peter J. McNamara

Publication date: 26 January 2011

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0907.2675

Mathematics Subject Classification ID

Representations of Lie and linear algebraic groups over local fields (22E50)

Related Items (24)

Non-generic unramified representations in metaplectic covering groups ⋮ Description of \(\mathsf {B}(\infty)\) through Kashiwara embedding for Lie algebra types \(E_6\) and \(E_7\) ⋮ Resonant Mirković-Vilonen polytopes and formulas for highest-weight characters ⋮ A combinatorial description of the Gindikin-Karpelevich formula in type \(A\) ⋮ The six-vertex model and deformations of the Weyl character formula ⋮ Weyl group multiple Dirichlet series, Eisenstein series and crystal bases ⋮ On the third moment of \(L(\frac{1}{2}, \chi_d)\). I: The rational function field case ⋮ Whittaker coefficients of metaplectic Eisenstein series ⋮ Tokuyama-type formulas for characters of type B ⋮ Young tableaux and crystal \(\mathcal B(\infty)\) for finite simple Lie algebras ⋮ On Iwahori-Whittaker functions for metaplectic groups ⋮ Representation theory of \(p\)-adic groups and canonical bases ⋮ Combinatorics of Casselman-Shalika formula in type $A$ ⋮ THE DOUBLE COVER OF ODD GENERAL SPIN GROUPS, SMALL REPRESENTATIONS, AND APPLICATIONS ⋮ Mappings for special functions on Cantor sets and special integral transforms via local fractional operators ⋮ Hecke \(L\)-functions and Fourier coefficients of covering Eisenstein series ⋮ The metaplectic Casselman-Shalika formula ⋮ On a conjecture about an analogue of Tokuyama's theorem for \(G_2\) ⋮ Unramified Whittaker functions for certain Brylinski-Deligne covering groups ⋮ PBW parametrizations and generalized preprojective algebras ⋮ Weyl group multiple Dirichlet series for symmetrizable Kac-Moody root systems ⋮ On the crystal graph description of the stable Weyl group multiple Dirichlet series ⋮ Crystal graphs, Tokuyama's theorem, and the Gindikin-Karpelevič formula for \(G_{2}\) ⋮ Local Coefficients and Gamma Factors for Principal Series of Covering Groups

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