Classification of one $\textsf K$-type representations

Abstract

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 spectrum when restricted to an Iwahori subgroup.

Locations

• Transactions of the American Mathematical Society - View - PDF