Conical Representations for Direct Limits of Symmetric Spaces
Abstract
We extend the definition of conical representations for Riemannian symmetric spaces to a certain class of infinitedimensional Riemannian symmetric spaces. Using an infinitedimensional version of Weyl's Unitary Trick, there is a correspondence between smooth representations of infinitedimensional noncompacttype Riemannian symmetric spaces and smooth representations of infinitedimensional compacttype symmetric spaces. We classify all smooth conical representations which are unitary on the compacttype side. Finally, a new class of nonsmooth unitary conical representations appears on the compacttype side which has no analogue in the finitedimensional case. We classify these representations and show how to decompose them into direct integrals of irreducible conical representations.
 Publication:

arXiv eprints
 Pub Date:
 November 2015
 arXiv:
 arXiv:1511.07045
 Bibcode:
 2015arXiv151107045D
 Keywords:

 Mathematics  Representation Theory;
 43A85;
 53C35;
 22E46
 EPrint:
 38 pages, 2 figures, 3 tables