This paper computes the Dirac cohomology HD(π) of irreducible unitary Harish-Chandra modules π complex classical groups viewed as real reductive groups. More precisely, representations with nonzero are shown to be unitarily induced from unipotent representations. When nonzero, there is a unique, multiplicity free K-type in contributing HD(π). confirms conjectures formulated by first named autho...

In this paper we will give the character table of the irreducible rational representations of G=SL (2, q) where q= , p prime, n>O, by using the character table and the Schur indices of SL(2,q).

In this paper we study representations of conformal nets associated with positive definite even lattices and their orbifolds with respect to isometries of the lattices. Using previous general results on orbifolds, we give a list of all irreducible representations of the orbifolds, which generate a unitary modular tensor category. 2000MSC:81R15, 17B69. Supported in part by NSF and a research gra...

The decomposition of unitary representations of a discrete group obtained by induction from a subgroup involves commensurators. In particular Mackey has shown that quasi-regular representations are irreducible if and only if the corresponding subgroups are self-commensurizing. The purpose of this work is to describe general constructions of pairs of groups ? 0 < ? with ? 0 its own commensurator...

In this paper, we define invariant tensor product and study invariant tensor products associated with discrete series representations. Let G(V1) × G(V2) be a pair of classical groups diagonally embedded in G(V1 ⊕ V2). Suppose that dimV1 < dimV2. Let π be a discrete series representation of G(V1 ⊕ V2). We prove that the functor π⊗G(V1) maps unitary representations of G(V1) to unitary representat...

Given a compact Kähler manifold, we consider the complement U of a divisor with normal crossings. We study the variety of unitary representations of π1(U) with certain restrictions related to the divisor. We show that the possible singularities of this variety as well as of the corresponding moduli space of irreducible representations are quadratic. In the course of our proof we exhibit a diffe...

Let G be the split solvable Lie group acting simply transitively on a Siegel domain D. We consider irreducible unitary representations of G realized on Hilbert spaces of holomorphic functions on D. We determine all such Hilbert spaces by connecting them with positive Riesz distributions on the dual cone and describe them through the Fourier-Laplace transform. Moreover we classify the representa...

One of the fundamental problems of abstract harmonic analysis is the determination of the irreducible unitary representations of simple Lie groups. After recalling why this problem is of interest, we discuss the present state of knowledge about it. In the language of Kirillov and Kostant, the problem nally is to \quantize" nilpotent coadjoint orbits.

In [Z1] S. Zelditch introduced an equivariant version of a pseudo-differential calculus on a hyperbolic Riemann surface. We recast his construction in terms of trilinear invariant functionals on irreducible unitary representations of PGL2(R). This allows us to use certain properties of these functionals in the study of the action of pseudodifferential operators on eigenfunctions of the Laplacia...

We use earlier results on the classification of the positive energy unitary irreducible representations of the N-extended D=4 conformal superalgebras su(2,2/N). These results are applied to the reduction of supersymmetries and to the classification of BPS and possibly protected states.