In this paper among many other things we prove that the topological left amenability and left amenability of a weighted hypergroup (K, ?) are equivalent. For a normal subgroup H of K, we define a weight function ?? on KIH and obtain connection between left amenability of (K, ?) and (K|H, ??). Let H be a compact subhypergroup of K. We define the weight function on K||H and obtain connection...

Let G be Sp(2n, F) (resp. SO(2n + 1, F)), where F is a p-adic field of characteristic zero. In this paper, we give a correspondence which associates to an irreducible representation of G an m-tuple of irreducible representations of lower rank symplectic (resp. orthogonal) groups based on the supercuspidal support of . We show that this correspondence respects the induction and Jacquet module fu...

This contribution describes a new class of arithmetic architectures for Galois fields GF (2k). The main applications of the architecture are public-key systems which are based on the discrete logarithm problem for elliptic curves. The architectures use a representation of the field GF (2k) as GF ((2n)m), where k = n · m. The approach explores bit parallel arithmetic in the subfield GF (2n), and...

Building on previous papers by Anantharaman-Delaroche (AD) we introduce and study the notion of AD-amenability for partial actions Fell bundles over discrete groups. We prove that cross-sectional C*-algebra a bundle is nuclear if only underlying unit fibre AD-amenable. If action globalisable, then it AD-amenable its globalisation Moreover, preserved (weak) equivalence and, using very recent ide...

We consider the action of H = O(p, q) on the matrix space Mp+q,n(R). We study a certain orbit O of H in the null cone N ⊆ Mp+q,n(R) which supports an eigendistribution dνO for H . Using some identities of Capelli type developed in the Appendix, we determine the structure of G̃ = Sp(2n,R)∼-cyclic module generated by dνO under the oscillator representation of G̃ (the metaplectic cover of G = Sp(2n(...

we survey the recent investigations on (bounded, sequential) approximate connesamenability and pseudo-connes amenability for dual banach algebras. we will discuss thecore problems concerning these notions and address the signi cance of any solutions to themto the development of the eld.

In this paper we study the modular structure of the permutation module H ) of the symmetric group S2n acting on set partitions of a set of size 2n into n sets each of size 2, defined over a field of odd characteristic p. In particular we characterize the vertices of the indecomposable summands of H ) and fully describe all of its indecomposable summands that lie in blocks of p-weight at most tw...

We define a Banach algebra A to be dual if A = (A∗) ∗ for a closed submodule A∗ of A∗. The class of dual Banach algebras includes all W ∗-algebras, but also all algebras M(G) for locally compact groups G, all algebras L(E) for reflexive Banach spaces E, as well as all biduals of Arens regular Banach algebras. The general impression is that amenable, dual Banach algebras are rather the exception...

In this paper, we investigate, for a locally compact groupG, the operator amenability of the Fourier-Stieltjes algebra B(G) and of the reduced Fourier-Stieltjes algebra Br(G). The natural conjecture is that any of these algebras is operator amenable if and only if G is compact. We partially prove this conjecture with mere operator amenability replaced by operator C-amenability for some constant...

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