Given a unitary representation T of a finite group G in C, write M for the variety of such representations which are unitary equivalent to T . The representation T is said to be frequent if the dimension of the variety M is maximal (among all representations of G in the same complex space). We prove that the irreducible representations are distributed, in the frequent representation (of large d...

Coherent state theory is shown to reproduce three categories of representations of the spectrum generating algebra for an algebraic model: (i) classical realizations which are the starting point for geometric quantization; (ii) induced unitary representations corresponding to prequantization; and (iii) irreducible unitary representations obtained in geometric quantization by choice of a polariz...

‎We first give bounds for domains where the unitarizabile subquotients can show up in the parabolically induced representations of classical $p$-adic groups‎. ‎Roughly‎, ‎they can show up only if the‎ ‎central character of the inducing irreducible cuspidal representation is dominated by the‎ ‎square root of the modular character of the minimal parabolic subgroup‎. ‎For unitarizable subquotients...

For an element x of the Cuntz algebra ON , define the isotropy subgroup Gx ≡ {g ∈ U(N) : αg(x) = x} of the unitary group U(N) with respect to the canonical action α of U(N) on ON . We have irreducible representations of the crossed product ONoGx by extending irreducible generalized permutative representations of ON and irreducible representation of Gx. ¿From this, the Peter-Weyl theorem for Gx ...

M. Hanzer and I. Matić have proved that the genuine unitary principal series representations of the metaplectic groups are irreducible. A simple consequence of that paper is a criterion for the irreducibility of the non-unitary principal series representations of the metaplectic groups that we give in this paper.

Starting from conventional Young operators we construct Hermitian operators which project orthogonally onto irreducible representations of the (special) unitary group.

We study unitary irreducible representations of Uq(SO(2, 1)) and Uq(SO(2, 3)) for q a root of unity, which are finite – dimensional. Among others, unitary representations corresponding to all classical one – particle representations with integral weights are found for q = eiπ/m and m large enough. In the ”massless” case with spin ≥ 1 in 4 dimensions, they are unitarizable only after factoring o...

We define exact functors from categories of Harish-Chandra modules for certain real classical groups to finite-dimensional modules over an associated graded affine Hecke algebra with parameters. We then study some of the basic properties of these functors. In particular, we show that they map irreducible spherical representations to irreducible spherical representations and, moreover, that they...

We use the notion of rank defined in an earlier paper (2007) to introduce and study two correspondences between small irreducible unitary representations of the split real simple Lie groups of types En, where n ∈ {6, 7}, and two reductive classical groups. We show that these correspondences classify all of the unitary representations of rank two (in the sense of our earlier paper) of these exce...