Explicit Hilbert spaces for certain unipotent representations III
Abstract
We consider the groups G which arise from real semisimple Jordan algebras via the Tits-Koecher-Kantor construction. Such a G is characterized by the fact that it admits a parabolic subgroup P=LN which is conjugate to its opposite, and for which the nilradical N is abelian. In this situation, the Levi component L has a finite number of orbits on N; and each orbit carries a measure which transforms by a character under L. By Mackey theory the space of L2-functions on each orbit carries a natural irreducible unitary representation of P, and we consider the following two problems: (1) Extend this representation of P to a unitary representation of G. (2) Decompose tensor products of the resulting representations.
Cite
@article{arxiv.math/0110339,
title = {Explicit Hilbert spaces for certain unipotent representations III},
author = {Alexander Dvorsky and Siddhartha Sahi},
journal= {arXiv preprint arXiv:math/0110339},
year = {2016}
}
Comments
35 pages; this is a continuation of math.RT/9904051