Harmonic analysis on the space of \(p\)-adic unitary Hermitian matrices, mainly for dyadic case

zbMath1430.11051arXiv1602.06127MaRDI QIDQ1708162

Yumiko Hironaka

Publication date: 4 April 2018

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

Full work available at URL: https://arxiv.org/abs/1602.06127

zbMATH Keywords

Hermitian matricesspherical functionsPlancherel formulaunitary groupsHall-Littlewood polynomialsdyadic fields

Mathematics Subject Classification ID

Representations of Lie and linear algebraic groups over local fields (22E50) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) (33D52) (p)-adic theory (11E95)

Related Items (1)

Spherical functions and local densities on the space of p-adic quaternion Hermitian forms

Cites Work

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• Spherical functions and local densities on Hermitian forms
• Orthogonal polynomials associated with root systems
• The Poincaré series of a Coxeter group
• Spherical functions on $p$-adic homogeneous spaces
• Spherical functions on U(2n)/ (U(n) × U(n)) and hermitian Siegel series
• Spherical functions on the space of $p$-adic unitary hermitian matrices II, the case of odd size
• SPHERICAL FUNCTIONS ON THE SPACE OF p-ADIC UNITARY HERMITIAN MATRICES
• THE SIEGEL SERIES AND SPHERICAL FUNCTIONS ON O(2n)/(O(n) × O(n))
• Hermitian Forms Over Local Fields

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