We extend the definition of conical representations for Riemannian symmetric space to a certain class of infinite-dimensional Riemannian symmetric spaces. Using an infinite-dimensional version of Weyl's Unitary Trick, there is a correspondence between smooth representations of infinite-dimensional noncompact-type Riemannian symmetric spaces and smooth representations of infinite-dimensional compact-type symmetric spaces. We classify all smooth conical representations which are unitary on the compact-type side. Finally, a new class of non-smooth unitary conical representations appears on the compact-type side which has no analogue in the finite-dimensional case. We classify these representations and show how to decompose them into direct integrals of irreducible conical representations.
| Identifer | oai:union.ndltd.org:LSU/oai:etd.lsu.edu:etd-07112014-182603 |
| Date | 29 July 2014 |
| Creators | Dawson, Matthew Glenn |
| Contributors | Olafsson, Gestur, Sengupta, Ambar N., He, Hongyu, Perlis, Robert V., Smolinsky, Lawrence J., Legoria, Joseph |
| Publisher | LSU |
| Source Sets | Louisiana State University |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lsu.edu/docs/available/etd-07112014-182603/ |
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