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Classification of one $\textsf K$-type representations
Suppose $G$ is a simple reductive $p$-adic group with Weyl group $W$. We give a classification of the irreducible representations of $W$ which can be extended to real hermitian representations of the associated graded Hecke algebra $\mathbb {H}$. Such representations correspond to unitary representations of $G$ which have a small …