Invariant differential operators on a semisimple symmetric space and finite multiplicities in a Plancherel formula

@inproceedings{Ban2006InvariantDO,
title={Invariant differential operators on a semisimple symmetric space and finite multiplicities in a Plancherel formula},
author={Erik P. van den Ban},
year={2006}
}

Erik P. van den Ban

Published 2006

Let G be a connected real semisimple Lie group with finite centre, and let z be an involutive automorphism of G. Put G'={x~G: z(x)=x}, and let H be a closed subgroup of G with (G'),cHcG'; here (G'), denotes the identity component of GL In this paper we investigate some properties of the algebra D(X) of invariant differential operators on the semisimple symmetric space X=G/H. Our main results are that the action of D(X) diagonalizes over the discrete part of L2(X) (Theorem 1.5), and that the… CONTINUE READING