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

2003/02/14 by Anne-Marie Aubert, Anne‐Marie Aubert, Aubert, Anne-Marie +2 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Representation Theory (math.RT) #math.OA #math.RT

paper · pdf · doi:10.48550/arxiv.math/0302169

39 pages. We have made some minor changes, and re-written part of the introduction

openalex publication_date 2003/02/14 · arxiv created 2004/10/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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).

Citations

• Fourier Transforms of Intertwining Operators and Plancherel Measures for GL(n)
• Rankin-Selberg Convolutions

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