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Journal of Lie Theory 28 (2018), No. 3, 865--884
Copyright Heldermann Verlag 2018

On Unitary Representations of Disconnected Real Reductive Groups

Domagoj Kovacevic
University of Zagreb, Faculty of Electrical Engineering and Computing, Unska 3, 10000 Zagreb, Croatia

Let G be the real reductive group and let G0 be the identity component. Let us assume that the unitary dual D(G0) is known. In this paper the unitary dual D(G) is constructed. Automorphisms of G0 generated by elements of G are the main ingredient of the construction. If the automorphism is outer, one has to consider the corresponding intertwining operators S. Operators S and their properties are analyzed in Section 5. Automorphisms of g0 are closely related to automorphisms of G0. They are investigated in Section 3. Automorphisms of so(4,4) are analyzed in Section 4.

Keywords: Real Lie groups, representations, disconnected groups, automorphisms.

MSC: 17B10, 22E47.

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