The Knapp-Stein dimension theorem for 𝑝-adic groups

Silberger, Allan J.

doi:10.1090/S0002-9939-1978-0492091-5

The Knapp-Stein dimension theorem for $p$-adic groups
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Proc. Amer. Math. Soc. 68 (1978), 243-246 Request permission

Correction: Proc. Amer. Math. Soc. 76 (1979), 169-170.

Abstract:

Knapp and Stein have proved for semisimple Lie groups that the dimension of the commuting algebra of an induced tempered representation equals the index of a certain reflection group in a larger group. A precise analogue of their result is stated and proved in this paper for p-adic groups.

References

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Harish-Chandra, Harmonic analysis on reductive $p$-adic groups, Harmonic analysis on homogeneous spaces (Proc. Sympos. Pure Math., Vol. XXVI, Williams Coll., Williamstown, Mass., 1972) Amer. Math. Soc., Providence, R.I., 1973, pp. 167–192. MR 0340486
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