We introduce inductive limits of compact quantum groups and their unitary representation theories. Those give a more explicit representation-theoretic meaning to our previous study quantization characters central probability measures in the asymptotic theory. also tensor product representations infinite-dimensional group. As by-product, we an interpretation certain transformations that play imp...

We prove a geometric version of a classical result on the characterization of an irreducible cuspidal automorphic representation of GLn(AE ) being the base change of a stable cuspidal representation of the quasi-split unitary group associated to the quadratic extension E/F , via the nonvanishing of certain period integrals, called being distinguished. We show that certain cohomology of an autom...

We study the way the unitary evolution of spin 1/2 particules can be represented in a counterfactual definiteness setting. More precisely, by representing the state of such a particule by a triplet of values corresponding to the supposedly pre-existing outcomes of some measurements (those corresponding to the three Pauli matrices), we analyse the evolution of our representation when some unitar...

Introduction. In this note, we will announce a characterization of a connected, simply connected Type I solvable Lie group, G, and present a complete description of the set of all unitary equivalence classes of irreducible unitary representations of G together with a construction of an irreducible representation in each equivalence class. This result subsumes the results previously obtained on ...

We present a new proof of the Poisson integral formula for harmonic functions using the methods of representation theory. In doing so, we exhibit the irreducible subspaces and unitary structure of a representation of the group SU(1, 1) of 2 × 2 complex generalized special unitary matrices. Our arguments illustrate a technique that can be used to prove similar reproducing formulas in higher dime...

We study closed subspaces of L(X ), where (X , μ) is a σ-finite measure space, that are invariant under the unitary representation associated to a measurable action of a discrete countable LCA group Γ on X . We provide a complete description for these spaces in terms of range functions and a suitable generalized Zak transform. As an application of our main result, we prove a characterization of...

The Wigner function provides a useful quasiprobability representation of quantum mechanics, with applications in various branches of physics. Many nice properties of the Wigner function are intimately connected with the high symmetry of the underlying operator basis composed of phase point operators: any pair of phase point operators can be transformed to any other pair by a unitary symmetry tr...

Harish-Chandra Collected Papers Edited by V. S. Varadarajan Volume 1: 1944–54 pp. 566 Volume 2: 1955–58 pp. 539 Volume 3: 1959–68 pp. 670 Volume 4: 1970–83 pp. 461 Group-representation theory is a broad topic which impinges on many domains of mathematics. The characters of abelian groups are of course central to Fourier analysis and entered at an early stage the theory of numbers, one of severa...

How can you find a complete set of inequivalent irreducible (ordinary) representations of a finite group? The theory is classical but, except when the group was very small or had a rather special structure, the actual computations were prohibitive before the advent of high-speed computers ; and there remain practical difficulties even for groups of relatively small orders ( á 100). The present ...

where P is a positive definite hermitian matrix and U is a unitary matrix. In this polar representation of the matrix A, as it is called, the two matrices P and U are unique. Since the matrix P is positive definite and nonsingular, it has the same signature as the identity matrix E while the unitary matrix U is a conjunctive automorph of E. From (1) we may deduce a somewhat similar representati...