Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Harish-Chandra's Plancherel theorem
for $ \mathfrak {p}$-adic groups

Author: Allan J. Silberger
Journal: Trans. Amer. Math. Soc. 348 (1996), 4673-4686
MSC (1991): Primary 22E50
Erratum: Trans. Amer. Math. Soc. 352 (2000), 1947-1949.
MathSciNet review: 1370652
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $G$ be a reductive $ \mathfrak {p}$-adic group. In his paper, ``The Plancherel Formula for Reductive $\mathfrak {p}$-adic Groups", Harish-Chandra summarized the theory underlying the Plancherel formula for $G$ and sketched a proof of the Plancherel theorem for $G$. One step in the proof, stated as Theorem 11 in Harish-Chandra's paper, has seemed an elusively difficult step for the reader to supply. In this paper we prove the Plancherel theorem, essentially, by proving a special case of Theorem 11. We close by deriving a version of Theorem 11 from the Plancherel theorem.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 22E50

Retrieve articles in all journals with MSC (1991): 22E50

Additional Information

Allan J. Silberger
Affiliation: Department of Mathematics, Cleveland State University, Cleveland, Ohio 44115

Keywords: Discrete series, induced representations, Plancherel theorem, reductive $ \mathfrak{p}$--adic group, Schwartz space, tempered representation
Received by editor(s): July 6, 1995
Received by editor(s) in revised form: December 15, 1995
Article copyright: © Copyright 1996 American Mathematical Society