Plancherel measure for GL(n,F) and GL(m,D): explicit formulas and Bernstein decomposition
Representation Theory
2007-05-23 v4 Operator Algebras
Abstract
Let F be a nonarchimedean local field, let D be a division algebra over F, let GL(n) = GL(n,F). Let \nu denote Plancherel measure for GL(n). Each component \Omega in the Bernstein variety \Omega(GL(n)) has several numerical invariants attached to it. We provide explicit formulas for the Bernstein component \nu_{\Omega} of Plancherel measure in terms of these invariants. We also prove some new formal degree formulas, a transfer-of-measure formula for GL(n), and a transfer-of-measure formula from GL(n,F) to GL(m,D).
Cite
@article{arxiv.math/0302169,
title = {Plancherel measure for GL(n,F) and GL(m,D): explicit formulas and Bernstein decomposition},
author = {Anne-Marie Aubert and Roger Plymen},
journal= {arXiv preprint arXiv:math/0302169},
year = {2007}
}
Comments
39 pages. We have made some minor changes, and re-written part of the introduction