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- W2962721836 abstract "We have been interested in the harmonic analysis on p-adic homogeneous spaces based on spherical functions. We have considered the space of p-adic unitary hermitian matrices of even size in [HK], and in the present article we will report that of odd size. For details, please see the full version [HK2]. The results can be formulated in parallel, though the groups acting the spaces have different root structures, Cn for even and BCn for odd. The spaces have a natural close relation to the theory of automorphic functions and classical theory of sesquilinear forms (e.g. [H3], [HS]). We fix an unramified quadratic extension k′/k of p-adic field k such that 2 / ∈ p, and consider hermitian and unitary matrices with respect to k′/k, and denote by a∗ the conjugate transpose of a ∈ Mmn(k). Let π be a prime element of k and q the cardinality of the residue class field Ok/(π) and we normalize the absolute value on k by |π| = q−1. Denote by jm ∈ GLm(k) the matrix whose all anti-diagonal entries are 1 and others are 0. Set" @default.
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- W2962721836 date "2014-03-15" @default.
- W2962721836 modified "2023-09-26" @default.
- W2962721836 title "Spherical Functions on the Space of p-adic Unitary Hermitian Matrices II, the Case of Odd Size" @default.
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