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Schur orthogonality relations and invariant sesquilinear forms

Author: Robert W. Donley Jr.
Journal: Proc. Amer. Math. Soc. 130 (2002), 1211-1219
MSC (2000): Primary 22D10, 22E46
Published electronically: August 29, 2001
MathSciNet review: 1873799
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Abstract: Important connections between the representation theory of a compact group $G$ and $L^{2}(G)$ are summarized by the Schur orthogonality relations. The first part of this work is to generalize these relations to all finite-dimensional representations of a connected semisimple Lie group $G.$ The second part establishes a general framework in the case of unitary representations $(\pi , V)$ of a separable locally compact group. The key step is to identify the matrix coefficient space with a dense subset of the Hilbert-Schmidt endomorphisms on $V$.

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Additional Information

Robert W. Donley Jr.
Affiliation: Department of Mathematics, University of North Texas, Denton, Texas 76203

Received by editor(s): September 25, 2000
Published electronically: August 29, 2001
Additional Notes: This work was partially supported by NSF grant DMS-9627447
Communicated by: Rebecca Herb
Article copyright: © Copyright 2001 American Mathematical Society