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2006.101: Reduced C*-algebra of the p-adic group GL(n) II

2006.101: Roger Plymen (2002) Reduced C*-algebra of the p-adic group GL(n) II. Journal of Functional Analysis, 196 (1). pp. 119-134. ISSN 0022-1236

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DOI: 10.1006/jfan.2002.3980


The reduced C*-algebra of the p-adic group GL(n) admits a Bernstein decomposition. We give a minimal refinement of this decomposition, and provide structure theorems for the reduced Iwahori-Hecke C*-algebra and the reduced spherical C*-algebra. This leads to a very explicit description of the tempered dual of GL(n) in terms of Bernstein parameters and extended quotients. We also prove that Plancherel measure (on the tempered dual of a reductive p-adic group) is rotation-invariant.

Item Type:Article
Uncontrolled Keywords:General linear group. Reduced C*-algebra. Tempered dual. Bernstein parameters. Plancherel measure
Subjects:MSC 2000 > 46 Functional analysis
MIMS number:2006.101
Deposited By:Professor Roger Plymen
Deposited On:18 May 2006

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