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De nition 2.0.1. A representation (;X) on a Hilbert space
X is called unitary if X admits a (nondegenerate) inner product
h ; i such that G acts by unitary transformations.
This paper discusses the role of the relevant and petite K-types in the
classi cation of the spherical unitary dual for split real groups.
Let G be the rational points of a connected linear reductiv...