A Trip to Group Representation Theory, Wroclaw Fall 2010 Tomasz Przebinda and the Participants

Howe’s Correspondence for a Generic Harmonic Analyst

The goal of this article is to explain Howe’s correspondence to a reader who is not necessarily an expert on Representation Theory of Real Reductive Groups, but is familiar with general concepts of Harmonic Analysis. We recall Howe’s construction of the Oscillator Representation, the notion of a dual pair and a few basic and general facts concerning the correspondence.

The Oscillator Character Formula, for Isometry Groups of Split Forms in Deep Stable Range

Andrzej Daszkiewicz and Tomasz Przebinda Department of Mathematics, N. Copernicus University, 87-100 Toruń, Poland Department of Mathematics, University of Oklahoma, Norman, OK, 73019, USA Abstract. Let e G and e G′ be a reductive dual pair of the type mentioned in the title, with e G the smaller member. Let Π and Π′ be unitary representations of e G, e G′ which occur in Howe’s correspondence. ...

The Cauchy Harish-chandra Integral, for the Pair

One of the main problems in the theory of dual pairs is the description of the correspondence of characters of representations in Howe duality, [H]. In [D-P] a formula describing this correspondence was obtained under some very strong assumptions. In [P] the second author has developed a notion of a Cauchy Harish-Chandra integral for any real reductive pair, in order to describe this correspond...

The optimal solutions to the continuous and discrete-time versions of the Hirschman uncertainty principle

A representation for some groups, a geometric approach

‎In the present paper‎, ‎we are going to use geometric and topological concepts‎, ‎entities and properties of the‎ ‎integral curves of linear vector fields‎, ‎and the theory of differential equations‎, ‎to establish a representation for some groups on $R^{n} (ngeq 1)$‎. ‎Among other things‎, ‎we investigate the surjectivity and faithfulness of the representation‎. At the end‎, ‎we give some app...