Vol. 125, No. 2, 1986

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Analytic continuation of local representations of Lie groups

Palle E. T. Jorgensen

Vol. 125 (1986), No. 2, 397–408

We consider a symmetric space (G,K,σ) where G is a Lie group, K a closed subgroup, and σ the involutive automorphism defining the space. A local representation π is defined for g in a neighborhood of e in G, and the operator π(g) is unbounded and defined on a dense subspace in a Hilbert space where the identity

π(g−1) = π(σ(g))∗

holds. We study analytic continuations of π to unitary representations of a group G which is dual to G.

Mathematical Subject Classification 2000
Primary: 22E45
Received: 3 July 1985
Published: 1 December 1986
Palle E. T. Jorgensen