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

Anne-Marie Aubert·Roger Plymen
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Abstract

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).

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BibTeXRIS

Anne-Marie Aubert, Roger Plymen. 2004-10-04. Plancherel measure for GL(n,F) and GL(m,D): explicit formulas and Bernstein decomposition. https://arxiv.org/abs/math/0302169

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