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

R. J. Plymen

doi:10.1006/jfan.2002.3980

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

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Abstract

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. © 2002 Elsevier Science (USA).

Original language	English
Pages (from-to)	119-134
Number of pages	15
Journal	Journal of Functional Analysis
Volume	196
Issue number	1
DOIs	https://doi.org/10.1006/jfan.2002.3980
Publication status	Published - 1 Dec 2002

Keywords

Bernstein parameters
Plancherel measure
Reduced C*-algebra
Tempered dual

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10.1006/jfan.2002.3980

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abstract = "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. {\textcopyright} 2002 Elsevier Science (USA).",

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N2 - 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. © 2002 Elsevier Science (USA).

AB - 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. © 2002 Elsevier Science (USA).

KW - Bernstein parameters

KW - Plancherel measure

KW - Reduced C-algebra

KW - Tempered dual

U2 - 10.1006/jfan.2002.3980

DO - 10.1006/jfan.2002.3980

M3 - Article

SN - 0022-1236

VL - 196

SP - 119

EP - 134

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 1

ER -

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

Abstract

Keywords

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