New formulas for Whittaker functions on \(\text{GL}(n,\mathbb R)\)

DOI10.1016/j.jfa.2006.12.004zbMath1121.22003OpenAlexW2012264678MaRDI QIDQ880096

Taku Ishii, Eric Stade

Publication date: 10 May 2007

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2006.12.004

zbMATH Keywords

Whittaker functionslinear group

Mathematics Subject Classification ID

Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Analysis on other specific Lie groups (43A80)

Related Items (17)

Archimedean zeta integrals on \(\mathrm{GL}_n\times\mathrm{GL}_m\) and \(\mathrm{SO}_{2n+1}\times\mathrm{GL}_m\) ⋮ The computation of multivariate archimedean zeta integrals on ${GL}_2 \times {GSp}_4$ and ${GL}_4$ ⋮ Calculus of archimedean Rankin–Selberg integrals with recurrence relations ⋮ Discrete Whittaker processes ⋮ Directed polymers and the quantum Toda lattice ⋮ HALF-SPACE MACDONALD PROCESSES ⋮ Survival probability of mutually killing Brownian motions and the O'Connell process ⋮ Archimedean zeta integrals for the exterior square \(L\)-functions on \(\mathrm{GL}_{n}\) ⋮ Recurrence relations for Mellin transforms of \(G L(n, \mathbb{R})\) Whittaker functions ⋮ Macdonald processes ⋮ Geometric RSK and the Toda lattice ⋮ Calculus of principal series Whittaker functions on \(\mathrm{SL}(n, \mathbb R)\) ⋮ Whittaker functions for generalized principal series representations of \(\mathrm{SL}(3, \mathbb R)\) ⋮ Baxter operator and archimedean Hecke algebra ⋮ Geometric RSK correspondence, Whittaker functions and symmetrized random polymers ⋮ Calculus of principal series Whittaker functions on \(\text{GL}(3,\mathbb C)\) ⋮ On the nonexistence of automorphic eigenfunctions of exponential growth on \(\mathrm{SL}(3,\mathbb Z)\setminus \mathrm{SL}(3,\mathbb R)/\mathrm{SO}(3,\mathbb R)\)

Cites Work

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• Whittaker functions on semisimple Lie groups
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• Poincaré series for GL(3,\({\mathbb{R}})\)-Whittaker functions
• On Mellin transforms of unramified Whittaker functions on GL(3,C)
• The multiplicity one theorem for \(\mathrm{GL}_n\)
• On Whittaker vectors and representation theory
• Archimedean \(L\)-factors on \(\text{GL}(n)\times\text{GL}(n)\) and generalized Barnes integrals
• A remark on Whittaker functions on SL\((n,{\mathbb R})\).
• Quantum cohomology of flag manifolds and Toda lattices
• Mellin transforms of Whittaker functions on \(\text{GL} (4,\mathbb{R})\) and \(\text{GL} (4,\mathbb{C})\)
• Mellin transforms of GL ( n , [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /) whittaker functions]
• Rankin-Selberg Convolutions
• Poincaré series and Kloosterman sums for SL(3, Z)
• The special values of the zeta functions associated with cusp forms
• Stationary Phase Integrals, Quantum Toda Lattices, Flag Manifolds and the Mirror Conjecture
• A class of nonanalytic automorphic functions
• Fonctions de Whittaker associées aux groupes de Chevalley

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