Principal Series Representations of Direct Limit Groups
Abstract
We combine the geometric realization of principal series representations of the author, with the BottBorelWeil Theorem for direct limits of compact groups of Natarajan, RodriguezCarrington and the author, obtaining limits of principal series representations for direct limits of real reductive Lie groups. We introduce the notion of weakly parabolic direct limits and relate it to the conditions that the limit representations are normpreserving representations on a Banach space or unitary representations on a Hilbert space. We specialize the results to diagonal embedding direct limit groups. Finally we discuss the possibilities of extending the results to limits of tempered series other than the principal series.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 2004
 arXiv:
 arXiv:math/0402283
 Bibcode:
 2004math......2283W
 Keywords:

 Representation Theory;
 Functional Analysis;
 22E30;
 22E46;
 22E65
 EPrint:
 28 pages