Tamely ramified supercuspidal representations of classical groups. II. Representation theory
Tensor products and p-induction of representations on Banach spaces.
In this paper we obtain Lp versions of the classical theorems of induced representations, namely, the inducing in stages theorem, the Kronecker product theorem, the Frobenius Reciprocity theorem and the subgroup theorem. In doing so we adopt the tensor product approach of Rieffel to inducing.
The Capelli identity and unitary representations
The Choquet-Deny theorem and distal properties of totally disconnected locally compact groups of polynomial growth.
The Clebsch-Gordan coefficients with respect to various bases for unitary and orthogonal representations of and .
The conjugation representation and inner amenability of discrete groups.
The Connes-Kasparov conjecture for almost connected groups and for linear -adic groups
Let G be a locally compact group with cocompact connected component. We prove that the assembly map from the topological K-theory of G to the K-theory of the reduced C*-algebra of G is an isomorphism. The same is shown for the groups of k-rational points of any linear algebraic group over a local field k of characteristic zero.
The density of the image of the exponential function and spacious locally compact groups.
The dual space of precompact groups
For any topological group the dual object is defined as the set of equivalence classes of irreducible unitary representations of equipped with the Fell topology. If is compact, is discrete. In an earlier paper we proved that is discrete for every metrizable precompact group, i.e. a dense subgroup of a compact metrizable group. We generalize this result to the case when is an almost metrizable precompact group.
The duality theorem for locally compact Abelian -groups.
The duality theorems. Cyclic representations Langlands conjectures [Book]
The elements of bounded trace in the C*-algebra of a nilpotent Lie group.
The energy representation of Sobolev-Lie groups
The failure of the topological Frobenius property for nilpotent Lie groups.
The Fourier algebra of SL(2,...)......, n...2, has no multiplier bounded approximate unit.
The Injection and the Protection Theorem for Spectral Sets
The irreducibility of restrictions of unitary representations of lattices.
The L...-representation algebra of a foundation topological semigroup.
The Mautner Phenomenon for p-adic Lie Groups.
The Norm-Strict Bidual of a Banach Algebra and the Dual of Cu(G).