Commutation relations of differential operators and Whittaker functions on \(\text{Sp}_ 2(\mathbb{R})\)

DOI10.3792/pjaa.71.189zbMath0868.11027OpenAlexW2031463242MaRDI QIDQ1917580

Shinji Niwa

Publication date: 19 August 1997

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.71.189

zbMATH Keywords

Mellin transformWeil representationcommutation relations of differential operatorsformula for Whittaker functions

Mathematics Subject Classification ID

Representation-theoretic methods; automorphic representations over local and global fields (11F70) Representations of Lie and linear algebraic groups over global fields and adèle rings (22E55)

Related Items (8)

Whittaker functions for generalized principal series representations of \(\mathrm{GSp}(2,\mathbb{R})\) ⋮ Archimedean zeta integrals on \(\mathrm{GL}_n\times\mathrm{GL}_m\) and \(\mathrm{SO}_{2n+1}\times\mathrm{GL}_m\) ⋮ Whittaker functions for \(P_J\)-principal series representations of \(\text{Sp}(3,\mathbb R)\) ⋮ Synchronized oscillation of the segmentation clock gene in vertebrate development ⋮ Principal series and generalized principal series Whittaker functions with peripheral \(K\)-types on the real symplectic group of rank 2 ⋮ Spinor $L$-functions for generic cusp forms on $GSp(2)$ belonging to principal series representations ⋮ Principal series Whittaker functions on \(Sp(2,\mathbb{C})\) ⋮ On principal series Whittaker functions on \(\text{Sp}(2,\mathbb R)\)

Cites Work

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• Whittaker functions on semisimple Lie groups
• On invariant differential operators on bounded symmetric domains of type IV
• Some examples of automorphic forms on Sp4
• Automorphic forms on GL(3,\({\mathbb{R}})\)
• An explicit integral representation of Whittaker functions on \(\text{Sp}(2;\mathbb{R})\) for the large discrete series representations
• Barnes' Second Lemma and its Application to Rankin-Selberg Convolutions
• On generalized Whittaker functions on Siegel’s upper half space of degree 2
• Eléments de Mathématique. Groupes et algèbres de Lie

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