Some examples of square integrable representations of semisimple 𝑝-adic groups

Lusztig, George

doi:10.1090/S0002-9947-1983-0694380-4

Some examples of square integrable representations of semisimple $p$-adic groups
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Trans. Amer. Math. Soc. 277 (1983), 623-653 Request permission

Abstract:

We construct irreducible representations of the Hecke algebra of an affine Weyl group analogous to Kilmoyer’s reflection representation corresponding to finite Weyl groups, and we show that in many cases they correspond to a square integrable representation of a simple $p$-adic group.

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