Weyl group multiple Dirichlet series, Eisenstein series and crystal bases

DOI10.4007/annals.2011.173.2.13zbMath1302.11032OpenAlexW2108069513MaRDI QIDQ640763

Daniel Bump, Solomon Friedberg, Benjamin Brubaker

Publication date: 20 October 2011

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4007/annals.2011.173.2.13

zbMATH Keywords

Eisenstein seriescrystal basesWeyl group multiple Dirichlet seriesEisenstein conjecture

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Dirichlet series in several complex variables associated to automorphic forms; Weyl group multiple Dirichlet series (11F68)

Related Items (28)

Connecting marginally large tableaux and rigged configurations via crystals ⋮ Parametrization of Kloosterman sets and \(\mathrm{SL}_3\)-Kloosterman sums ⋮ Distinguished theta representations for certain covering groups ⋮ On Hamiltonians for six-vertex models ⋮ Resonant Mirković-Vilonen polytopes and formulas for highest-weight characters ⋮ Secondary terms in the asymptotics of moments of \(L\)-functions ⋮ Planes in Z4$\mathbb {Z}^4$ and Eisenstein series ⋮ The six-vertex model and deformations of the Weyl character formula ⋮ On the third moment of \(L(\frac{1}{2}, \chi_d)\). I: The rational function field case ⋮ Metaplectic theta functions and global integrals ⋮ Schur polynomials and the Yang-Baxter equation ⋮ The flush statistic on semistandard Young tableaux ⋮ A survey on the theory of multiple Dirichlet series with arithmetical coefficients as numerators ⋮ Whittaker coefficients of metaplectic Eisenstein series ⋮ Tokuyama-type formulas for characters of type B ⋮ On Iwahori-Whittaker functions for metaplectic groups ⋮ Representation theory of \(p\)-adic groups and canonical bases ⋮ Combinatorics of Casselman-Shalika formula in type $A$ ⋮ Constructing Weyl group multiple Dirichlet series ⋮ Affine Weyl Group Multiple Dirichlet Series: Type $\tilde{A}$ ⋮ Hecke \(L\)-functions and Fourier coefficients of covering Eisenstein series ⋮ On the third moment of \(L(\frac{1}{2},\chi_d)\). II: The number field case ⋮ Metaplectic representations of Hecke algebras, Weyl group actions, and associated polynomials ⋮ Convergence formulae for double Dirichlet series ⋮ Unramified Whittaker functions for certain Brylinski-Deligne covering groups ⋮ Weyl group multiple Dirichlet series for symmetrizable Kac-Moody root systems ⋮ On the crystal graph description of the stable Weyl group multiple Dirichlet series ⋮ The Fourier coefficients of a metaplectic Eisenstein distribution on the double cover of SL(3) over \(\mathbb{Q} \)

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