论文信息 - On square-integrable representations and the coadjoint action of solvable Lie groups

On square-integrable representations and the coadjoint action of solvable Lie groups

In terms of the bijective Pukánszky correspondence between the generalized orbits of the coadjoint action and the quasi-equivalence classes of normal representations of solvable Lie groups, we determine the orbits that correspond to square-integrable representations. We then characterize the type I property of square integrable representations in terms of the coadjoint action and we prove that the isolated points of the primitive ideal space are type I when the nilradical has codimension 1. This fact does not hold true for codimension > 2, as shown by specific examples of solvable Lie groups that have dense coadjoint orbits which are not locally closed. The case of the 2-codimensional nilradical is left open.

Ingrid Beltita | Daniel Beltita

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