It is well-known that one of the most important ways of constructing cohomology for an arithmetic quotient Γ\X, where X is the symmetric space associated with a semi-simple Lie group G with finite center and Γ is a discrete subgroup of G, is through the use of Matsushima’s formula, namely by exhibiting irreducible unitary representations with non-zero continuous cohomology which occur in L2(Γ\G...

In recent years, a lively debate in neuroeconomics has focused on what appears to be a fundamental question: Is the brain a unitary or a dual system? We are still far from a consensus view. The accumulating evidence supports both sides of the debate. A reason for the difficulty in reaching a convincing solution is that we do not yet have a clear theoretical model for either position. Here I rev...

Introduction. A great deal of work has been done in the last fifteen years on the theory and classification of irreducible unitary representations of locally compact groups. It is also generally recognized (see for example [12, § 8]) that, at least for some classes of groups, it is artificial to confine oneself to unitary representations; one ought to study the irreducible Banach space represen...

For any unitary representation of an arbitrary Lie group I construct a moment mapping from the space of smooth vectors of the representation into the dual of the Lie algebra. This moment mapping is equivariant and smooth. For the space of analytic vectors the same construction is possible and leads to a real analytic moment mapping.

In this paper we give an explicit parameterization of the local theta correspondence of supercuspidal representations for the reductive dual pairs (U1(F ),U1(F )), (U1(F ),U1,1(F )), (U1(F ),U2(F )), and (U1(F ),U1,2(F )) of unitary groups over a nonarchimedean local field F of odd residue characteristic.

We classify pseudo-unitary modular categories of rank at most 5 under the assumption that some simple object is not isomorphic to its dual. Our approach uses Gröbner basis computations, and suggests a general computational procedure for classifying low-rank modular categories.

We show the uniqueness and disjointness of Klyachko models for GLn over a non-archimedean local field. This completes, in particular, the study of Klyachko models on the unitary dual. Our local results imply a global rigidity property for the discrete automorphic spectrum.

Angle estimation for a bistatic MIMO radar system based on Unitary Esprit techniques is proposed in this study. The algorithm exploits the dual invariance in distinct directions and centrosymmetry of the bistatic MIMO radar system to provide real valued computations and automatically paired Directions of Departures (DOD) and Directions of Arrival (DOA) estimates. Simulation results show the eff...

Angle estimation for a bistatic MIMO radar system based on Unitary Esprit techniques is proposed in this study. The algorithm exploits the dual invariance in distinct directions and centrosymmetry of the bistatic MIMO radar system to provide real valued computations and automatically paired Directions of Departures (DOD) and Directions of Arrival (DOA) estimates. Simulation results show the eff...