## 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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## 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.

Item Type: | Article |
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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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