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A short proof of the Selberg principle for a \(p\)-adic group. (Une preuve courte du principe de Selberg pour un groupe \(p\)-adique.) (French) Zbl 0978.22018
Let \(F\) be a local field of characteristic zero, \(G\) be the group of \(F\)-points of a reductive algebraic group defined over \(F\). The “abstract Selberg principle” proved by P. Blanc and J.-L. Brylinski [J. Funct. Anal. 109, 289-330 (1992; Zbl 0783.55004)] states that the orbital integrals of the Hattori rank of a finitely generated projective smooth representation of \(G\) over the conjugacy classes of the non-compact elements vanish.
The author gives a new proof based on Clozel’s integration formula [L. Clozel, Ann. Math. (2) 129, 237-251 (1989; Zbl 0675.22007)] and some \(K\)-theoretic arguments.

MSC:
22E50 Representations of Lie and linear algebraic groups over local fields
22E35 Analysis on \(p\)-adic Lie groups
19A49 \(K_0\) of other rings
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