Archimedean zeta integrals for 𝐺𝐿(3)×𝐺𝐿(2)

DOI10.1090/memo/1366OpenAlexW4281290132MaRDI QIDQ5097135

Taku Ishii, Tadashi Miyazaki, Miki Hirano

Publication date: 19 August 2022

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

Full work available at URL: https://doi.org/10.1090/memo/1366

zbMATH Keywords

automorphic formsWhittaker functionszeta integrals

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to number theory (11-02) Semisimple Lie groups and their representations (22E46) Fourier coefficients of automorphic forms (11F30) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Related Items (3)

Calculus of archimedean Rankin–Selberg integrals with recurrence relations ⋮ Rankin-Selberg convolutions for \(\mathrm{GL}(n) \times \mathrm{GL}(n)\) and \(\mathrm{GL} (n) \times \mathrm{GL} (n -1)\) for principal series representations ⋮ Test vectors for Archimedean period integrals

Cites Work

• Whittaker vectors and the Goodman-Wallach operators
• Automorphic forms on GL(3,\({\mathbb{R}})\)
• The Capelli identity, the double commutant theorem, and multiplicity-free actions
• Whittaker newforms for archimedean representations of GL(2)
• Whittaker functions for generalized principal series representations of \(\mathrm{SL}(3, \mathbb R)\)
• Calculus of principal series Whittaker functions on \(\text{GL}(3,\mathbb C)\)
• Reducibility of generalized principal series representations
• The multiplicity one theorem for \(\mathrm{GL}_n\)
• Gelfand-Kirillov dimension for Harish-Chandra modules
• On Whittaker vectors and representation theory
• The local zeta integrals for \(\mathrm{GL}(2,\mathbb{C})\times \mathrm{GL}(2,\mathbb{C})\)
• The homology of the connective \(K\)-theory spectrum as an \(\mathcal{A}(1)\)-module
• Automorphic forms on GL (2)
• Automorphic forms on \(\mathrm{GL}(2)\). Part II
• Mellin transforms of GL ( n , [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /) whittaker functions]
• THE CRITICAL VALUES OF RANKIN–SELBERG CONVOLUTIONS
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