Plancherel measure for GL(n,F) and GL(m,D): explicit formulas and Bernstein decomposition
Anne-Marie Aubert, Roger Plymen
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 νΩ 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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