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

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Let F be a nonarchimedean local field, let D be a division algebra over F, let GL(n) = GL(n,F). Let νdenote Plancherel measure for GL(n). Each component Ωin the Bernstein variety Ω(GL(n)) has several numerical invariants attached to it. We provide explicit formulas for the Bernstein component ν_Ω 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).
39 pages. We have made some minor changes, and re-written part of the introduction

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Representation Theory, Operator Algebras

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http://salesiana.dossiersoluciones.com/handle/123456789/66527

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0302169
 http://arxiv.org/abs/math/0302169

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arXiv