Spherical Functions and Local Densities of Alternating Forms

DOI10.2307/2374620zbMath0662.22013OpenAlexW2329313788MaRDI QIDQ3810864

Fumihiro Sato, Yumiko Hironaka

Publication date: 1988

Published in: American Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2374620

zbMATH Keywords

Plancherel measurespherical functionsconvolution operatorsHecke algebraprehomogeneous vector spaceHall-Littlewood polynomialsspherical Fourier transformlocal zeta functionsp-adic number field

Mathematics Subject Classification ID

Analytic theory (Epstein zeta functions; relations with automorphic forms and functions) (11E45) Analysis on (p)-adic Lie groups (22E35) Representations of Lie and linear algebraic groups over local fields (22E50) Harmonic analysis and spherical functions (43A90)

Related Items (13)

Spherical functions and local densities on the space of p-adic quaternion Hermitian forms ⋮ Asymptotics of functions on a \(p\)-adic reductive symmetric space ⋮ Whittaker-Shintani function for orthogonal groups ⋮ A \(p\)-adic interpretation of some integral identities for Hall-Littlewood polynomials ⋮ SPHERICAL FUNCTIONS ON THE SPACE OF p-ADIC UNITARY HERMITIAN MATRICES ⋮ Constant term of functions on a \(p\)-adic reductive symmetric space ⋮ \(H\)-invariant distribution vectors of induced representations for a \(p\)-adic reductive symmetric space \(G/H\) ⋮ Spherical functions on \(\text{Sp}_2\) as a spherical homogeneous \(\text{Sp}_2\times (\text{Sp}_1)^2\)-space ⋮ A Plancherel formula for Sp_2n/Sp_n×Sp_n and its application ⋮ Local zeta functions on Hermitian forms and its application to local densities ⋮ Local densities of alternating forms ⋮ Group schemes and local densities. ⋮ Functional equations of spherical functions on \(p\)-adic homogeneous spaces

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