We extend the Wigner distribution (WD) to conjugate unitary operators A, and Bp. The resulting “ABWD” is defined both as an a-b representation and as a timefrequency representation. Important properties and relations of the WD are generalized to the AB-WD.

The coherent states for the quantum particle on the circle are introduced. The Bargmann representation within the actual treatment provides the representation of the algebra [Ĵ , U ] = U , where U is unitary, which is a direct consequence of the Heisenberg algebra [φ̂, Ĵ ] = i, but it is more adequate for the study of the circlular motion.

The Langlands classiication theorem describes all admissible representations of a reductive group G in terms of the tempered representations of Levi subgroups of G. I will describe work with Susana Salamanca-Riba that provides (conjecturally) a similar description of the unitary representations of G in terms of certain very special unitary representations of Levi subgroups. x1. Introduction Sup...

Let lambda be a partition, with l parts, and let F(lambda) be the irreducible finite dimensional representation of GL(m) associated to lambda when l < or = m. The Littlewood Restriction Rule describes how F(lambda) decomposes when restricted to the orthogonal group O(m) or to the symplectic group Sp(m2) under the condition that l < or = m2. In this paper, this result is extended to all partitio...

The indefinite orthogonal group G = O(p, q) has a distinguished infinite dimensional irreducible unitary representation π for p+ q even and greater than 4, which is the “smallest” in the sense that the Gelfand–Kirillov dimension of π attains its (positive) minimum value p + q − 3 among the unitary dual of G. Moreover, π is the minimal representation if p+ q > 6. The Schrödinger model realizes π...

In this paper an implicit (double) shifted QR-method for computing the eigenvalues of companion and fellow matrices will be presented. Companion and fellow matrices are Hessenberg matrices, that can be decomposed into the sum of a unitary and a rank 1 matrix. The Hessenberg, the unitary as well as the rank 1 structures are preserved under a step of the QR-method. This makes these matrices suita...