The University of Southampton
University of Southampton Institutional Repository

# Plancherel measure for GL(n,F) and GL(m,D): explicit formulas and Bernstein decomposition

Aubert, Anne-Marie and Plymen, Roger (2005) Plancherel measure for GL(n,F) and GL(m,D): explicit formulas and Bernstein decomposition. Journal of Number Theory, 112 (1), 26-66.

Record type: Article

## Abstract

Let F be a nonarchimedean local field, let D be a division algebra over F, let GL(n)=GL(n,F). Let ? denote Plancherel measure for GL(n). Let ? be a component in the Bernstein variety ?(GL(n)). Then ? yields its fundamental invariants: the cardinality q of the residue field of F, the sizes m1,…,mt, exponents e1,…,et, torsion numbers r1,…,rt, formal degrees d1,…,dt and conductors f11,…,ftt. We provide explicit formulas for the Bernstein component ?? of Plancherel measure in terms of the fundamental invariants. We prove a transfer-of-measure formula for GL(n) and establish some new formal degree formulas. We derive, via the Jacquet–Langlands correspondence, the explicit Plancherel formula for GL(m,D).

Full text not available from this repository.

Published date: May 2005
Organisations: Pure Mathematics

## Identifiers

Local EPrints ID: 359950
URI: https://eprints.soton.ac.uk/id/eprint/359950
ISSN: 0022-314X
PURE UUID: 8e5451b6-5c79-429b-be29-a7b32c5341d2

## Catalogue record

Date deposited: 19 Nov 2013 14:02

## Contributors

Author: Anne-Marie Aubert
Author: Roger Plymen