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We give a conjectural description of the restriction of an irreducible representation of a unitary group U(n) to a subgroup U(n − 1) over a local or global field. We formulate analogous conjectures for the restriction problem from U(n) to a subgroup U(m) (m < n) using Bessel and Fourier-Jacobi models, and also similar restriction problems for symplectic… (More)
We use the recent proof of Jacquet’s conjecture due to Harris and Kudla, and the Burger-Sarnak principle to give a proof about the relationship between the existence of trilinear forms on representations of GL2(ku) for a non-Archimedean local field ku and local epsilon factors which was earlier proved only in the odd residue characteristic by this author in… (More)
Methods of theta correspondence are used to analyze local and global Bessel models for GSp4 proving a conjecture of Gross and Prasad which describes these models in terms of local epsilon factors in the local case, and the nonvanishing of central critical L-value in the global case.
We prove several multiplicity one theorems in this paper. For k a local field not of characteristic two, and V a symplectic space over k, any irreducible admissible representation of the symplectic similitude group GSp(V ) decomposes with multiplicity one when restricted to the symplectic group Sp(V ). We prove the analogous result for GO(V ) and O(V ),… (More)
In this paper we continue the study of locally analytic representations of a p-adic Lie group G in vector spaces over a spherically complete non-archimedean field K. In [ST], we began with an algebraic approach to this type of representation theory based on a duality functor that replaces locally analytic representations by certain topological modules over… (More)
We consider an Archimedean analogue of Tate’s conjecture, and verify the conjecture in the examples of isospectral Riemann surfaces constructed by Vignéras and Sunada. We prove a simple lemma in group theory which lies at the heart of T. Sunada’s theorem about isospectral manifolds. r 2002 Elsevier Science (USA). All rights reserved. MSC: primary 58G25;… (More)
Let E be an elliptic curve defined over Q. Let E(Fp) denote the elliptic curve modulo p. It is known that there exist integers i p and f p such that E(Fp) ∼= Z/ i pZ × Z/ i p f pZ. We study questions related to i p and f p . In particular, for any α > 0 and k ∈ N, we prove there exist positive constants cα and ck such that for any A > 0 ∑ p≤x (log i p) α =… (More)
In this paper we study the theta correspondence for Unitary groups of the same size over local and global fields. This correspondence has been studied in many cases by several authors. We are able to unify and generalise all these known results in terms of two conjectures, one local and the other global. These conjectures are in terms of the parametrisation… (More)
In this paper we prove a conjecture of Jacquet about supercuspidal representations of GLn(K ) distinguished by GLn(k), or by Un(k), for K a quadratic unramified extension of a non-Archimedean local field k.