The dual topology for the principal and discrete series on semisimple groups
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- by Ronald L. Lipsman
- Trans. Amer. Math. Soc. 152 (1970), 399-417
- DOI: https://doi.org/10.1090/S0002-9947-1970-0269778-X
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Abstract:
For a locally compact group $G$, the dual space $\hat G$ is the set of unitary equivalence classes of irreducible unitary representations equipped with the hull-kernel topology. We prove three results about $\hat G$ in the case that $G$ is a semisimple Lie group: (1) the irreducible principal series forms a Hausdorff subspace of $\hat G$; (2) the “discrete series” of square-integrable representations does in fact inherit the discrete topology from $\hat G$; (3) the topology of the reduced dual ${\hat G_r}$, that is the support of the Plancherel measure, is computed explicitly for split-rank 1 groups.References
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Bibliographic Information
- © Copyright 1970 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 152 (1970), 399-417
- MSC: Primary 22.60
- DOI: https://doi.org/10.1090/S0002-9947-1970-0269778-X
- MathSciNet review: 0269778