Identifier
etd-07112014-182603
Degree
Doctor of Philosophy (PhD)
Department
Mathematics
Document Type
Dissertation
Abstract
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.
Date
2014
Document Availability at the Time of Submission
Release the entire work immediately for access worldwide.
Recommended Citation
Dawson, Matthew Glenn, "Conical Representations for Direct Limits of Riemannian Symmetric Spaces." (2014). LSU Doctoral Dissertations. 2094.
https://repository.lsu.edu/gradschool_dissertations/2094
Committee Chair
Olafsson, Gestur
DOI
10.31390/gradschool_dissertations.2094