Document Type

Article

Publication Date

8-1-2017

Abstract

We extend the definition of conical representations for Riemannian symmetric spaces to a certain class of infinite-dimensional Riemannian symmetric spaces. Using a certain infinite-dimensional version of Weyl’s Unitary Trick, we show that 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.

Publication Source (Journal or Book title)

Mathematische Zeitschrift

First Page

1375

Last Page

1419

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