Eric Opdam
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.On the tempered L-function conjecture.
Mon, 08/31/2009 - 17:16 — SomNambulAuthors: Volker Heiermann, Eric Opdam
Subjects: Number Theory
AbstractWe give a general proof of Shahidi's tempered L-function conjecture, which
has previously been known in all but one case. One of the consequences is the
standard modules conjecture for p-adic groups, which means that the Langlands
quotient of a standard module is generic if and only if the standard module is
irreducible and the inducing data generic.On the tempered L-function conjecture.
Mon, 08/31/2009 - 17:16 — SomNambulAuthors: Volker Heiermann, Eric Opdam
Subjects: Number Theory
AbstractWe give a general proof of Shahidi's tempered L-function conjecture, which
has previously been known in all but one case. One of the consequences is the
standard modules conjecture for p-adic groups, which means that the Langlands
quotient of a standard module is generic if and only if the standard module is
irreducible and the inducing data generic.
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