Combinatorics of Casselman-Shalika formula in type $A$

DOI10.1090/S0002-9939-2014-11961-7zbMath1329.22009arXiv1111.1134MaRDI QIDQ5418541

Philip Lombardo, Kyu-Hwan Lee, Ben Salisbury

Publication date: 4 June 2014

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.1134

zbMATH Keywords

Young tableauxcrystalsCasselman-Shalika formula

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Analysis on (p)-adic Lie groups (22E35) Dirichlet series in several complex variables associated to automorphic forms; Weyl group multiple Dirichlet series (11F68)

Related Items (4)

Zigzag strip bundles and highest weight crystals ⋮ The flush statistic on semistandard Young tableaux ⋮ Young tableaux and crystal \(\mathcal B(\infty)\) for finite simple Lie algebras ⋮ Hecke \(L\)-functions and Fourier coefficients of covering Eisenstein series

Uses Software

• SageMath
• Sage-Combinat

Cites Work

• A combinatorial description of the Gindikin-Karpelevich formula in type \(A\)
• 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
• Weyl group multiple Dirichlet series, Eisenstein series and crystal bases
• Crystal graphs for representations of the \(q\)-analogue of classical Lie algebras
• Tensor product multiplicities, canonical and totally positive varieties
• The crystal structure on the set of Mirković-Vilonen polytopes
• Weyl Group Multiple Dirichlet Series
• Integration on $p$-adic groups and crystal bases
• Constructing Weyl group multiple Dirichlet series
• A Crystal Definition for Symplectic Multiple Dirichlet Series
• Littelmann Patterns and Weyl Group Multiple Dirichlet Series of Type D
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