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

DOI10.1016/j.jnt.2005.01.005zbMath1063.22015arXivmath/0302169OpenAlexW2011995297MaRDI QIDQ1775569

Roger Plymen, Anne-Marie Aubert

Publication date: 4 May 2005

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0302169

zbMATH Keywords

Plancherel measureBernstein decompositionDivision algebraLocal harmonic analysis

Mathematics Subject Classification ID

Representations of Lie and linear algebraic groups over local fields (22E50) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Zeta functions and (L)-functions (11S40)

Related Items (13)

Explicit Plancherel formula for the \(p\)-adic group GL(\(n\)) ⋮ On an inequality of Bushnell-Henniart for Rankin-Selberg conductors ⋮ A spectral decomposition of orbital integrals for \(PGL(2,F)\) (with an appendix by S. Debacker) ⋮ Automorphic Plancherel density theorem ⋮ Fields of rationality of cusp forms ⋮ BEYOND ENDOSCOPY FOR THE RELATIVE TRACE FORMULA II: GLOBAL THEORY ⋮ On calibrated representations and the Plancherel theorem for affine Hecke algebras ⋮ Geometric structure in the representation theory of \(p\)-adic groups ⋮ Formal degrees and adjoint 𝛾-factors ⋮ The formal degree of the discrete series representations of \(\mathrm{GL}_m(D)\) ⋮ Fields of rationality of automorphic representations: the case of unitary groups ⋮ Une remarque sur le degré formel d’une série discrète d’un groupe linéaire général $p$-adique ⋮ Formal degrees and the local theta correspondence: The quaternionic case

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