Patrick Delorme
Formule de Plancherel pour les fonctions de Whittaker sur un groupe r\'eductif $p$-adique.
Thu, 05/13/2010 - 15:01 — SomNambulAuthors: Patrick Delorme
Subjects: Representation Theory
AbstractWe prove the Plancherel formula for Whittaker functions on a reductive p-adic
group. This a sequel to our work on Paley-Wiener theorem. Our proof is close to
the proof written by Waldspurger of the Harish-Chandra Plancherel formula for
smooth functions on the group and use many of his results. One simplification
is the easy proof of the Fourier transfom, which follows from a result of
Joseph Bernstein.Analytic R-groups of affine Hecke algebras.
Tue, 09/08/2009 - 12:16 — SomNambulAuthors: Eric Opdam, Patrick Delorme
Subjects: Representation Theory
AbstractWe define analytic $R$-groups for affine Hecke algebras, and prove the analog
of the Knapp-Stein Dimension Theorem. As a corollary we prove that the
commutant algebra of a unitary principal series representation is isomorphic to
the complex group algebra of the $R$-group, twisted by a certain 2-cocycle
$\gamma$. For classical Hecke algebras we prove that $\gamma$ is always
trivial.Analytic R-groups of affine Hecke algebras.
Tue, 09/08/2009 - 12:16 — SomNambulAuthors: Eric Opdam, Patrick Delorme
Subjects: Representation Theory
AbstractWe define analytic $R$-groups for affine Hecke algebras, and prove the analog
of the Knapp-Stein Dimension Theorem. As a corollary we prove that the
commutant algebra of a unitary principal series representation is isomorphic to
the complex group algebra of the $R$-group, twisted by a certain 2-cocycle
$\gamma$. For classical Hecke algebras we prove that $\gamma$ is always
trivial.
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