Isolated points in duals of certain locally compact groups |
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Authors: | Terje Sund |
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Institution: | (1) Institute of Mathematics, University of Oslo, Blindern-Oslo 3, Norway |
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Abstract: | Summary LetG be a separable locally compact group with dual space. consists of all equivalence classes of irreducible unitary representations ofG, and is endowed with the Fell-topology. We study the topological properties in of the square-integrable representations ofG. is square-integrable provided there is a coordinate functiong((g)v, v),gG, for which is inL
2(G) w.r.t. left Haar measure onG.]SupposeG contains an open normal subgroupN of the formeKN
n
e whereK is compact. (All groups with a compact invariant neighborhood of the identity, IN] groups, satisfy this condition.) In this case we show that if is square-integrable then {} is an open point of.Finally, our techniques are used to prove this result for arbitrary (non connected) nilpotent Lie groups. |
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