Calculus of principal series Whittaker functions on \(\text{GL}(3,\mathbb C)\)

DOI10.1016/j.jfa.2008.10.011zbMath1166.22008OpenAlexW1978718153MaRDI QIDQ1017707

Takayuki Oda, Miki Hirano

Publication date: 12 May 2009

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

Full work available at URL: https://doi.org/10.1016/j.jfa.2008.10.011

zbMATH Keywords

Clebsch-Gordan coefficientWhittaker functionprincipal series representationDirac-Schmid operatorGelfand-Zelevinsky basis

Mathematics Subject Classification ID

Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) (43A65) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45)

Related Items (5)

Archimedean zeta integrals for 𝐺𝐿(3)×𝐺𝐿(2) ⋮ Principal series and generalized principal series Whittaker functions with peripheral \(K\)-types on the real symplectic group of rank 2 ⋮ On Deligne's conjecture for symmetric fourth \(L\)-functions of Hilbert modular forms ⋮ Calculus of principal series Whittaker functions on \(\mathrm{SL}(n, \mathbb R)\) ⋮ Whittaker functions for generalized principal series representations of \(\mathrm{SL}(3, \mathbb R)\)

Cites Work

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• Automorphic forms on GL(3,\({\mathbb{R}})\)
• The Capelli identity, the double commutant theorem, and multiplicity-free actions
• New formulas for Whittaker functions on \(\text{GL}(n,\mathbb R)\)
• Poincaré series for GL(3,\({\mathbb{R}})\)-Whittaker functions
• Automorphic functions and the Bass-Milnor-Serre homomorphism. I
• Theory of Eisenstein series for the group SL(3,R) and its application to a binary problem
• The multiplicity one theorem for \(\mathrm{GL}_n\)
• A remark on Whittaker functions on SL\((n,{\mathbb R})\).
• Lectures on automorphic \(L\)-functions
• Mellin transforms of Whittaker functions on \(\text{GL} (4,\mathbb{R})\) and \(\text{GL} (4,\mathbb{C})\)
• A definition of boundary values of solutions of partial differential equations with regular singularities
• Dirichlet series and automorphic forms
• Automorphic forms on GL (2)
• Mellin transforms of GL ( n , [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /) whittaker functions]
• On an explicit formula for class-$1$ “Whittaker functions” on $GL_n $ over $\beta $-adic fields
• Fonctions de Whittaker associées aux groupes de Chevalley

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