On Harish-Chandra’s 𝜇-function for 𝑝-adic groups

Silberger, Allan J.

doi:10.1090/S0002-9947-1980-0570781-7

On Harish-Chandra’s $\mu$-function for $p$-adic groups
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by Allan J. Silberger PDF

Trans. Amer. Math. Soc. 260 (1980), 113-121 Request permission

Abstract:

The Harish-Chandra $\mu$-function is, up to known constant factors, the Plancherel’s measure associated to an induced series of representations. In this paper we show that, when the series is induced from special representations lifted to a parabolic subgroup, the $\mu$-function is a quotient of translated $\mu$-functions associated to series induced from supercuspidal representations. It is now known, in both the real and p-adic cases, that the $\mu$-function is always an Euler factor.

References

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Special representations of reductive p-adic groups are not integrable

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