Original scientific paper

Sur une conjecture de Tadic

A. I. Badulescu
D. A. Renard

Abstract

Let F be a non-archimedian field of characteristic zero and D a central division algebra over F of finite dimension d2. For all positive integer r, set G'r = GL(r,D).
In 1990, M. Tadic gave a conjectural classification of the unitary dual of the G'r, and five statements denoted U0, ... , U4, which imply the classification. M. Tadic proved U3 and U4. Also, U0 and U1 imply U2. These statements, and the resulting classification are the natural generalization of the case D = F completely solved by M. Tadic in 1986. Here we prove U1. Thus, the classification of the unitary dual of the G'r is now reduced to the conjecture U0, which states that a parabolically induced representation from an irreducible unitary representation is irreducible.

Keywords

Representations of p-adic groups; unitary dual

Hrčak ID:

1262

URI

https://hrcak.srce.hr/1262

Publication date:

1.6.2004.

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