Miércoles 22 de Julio, 14:30-16:40. IMA-PUCV

Expositor: Anne-Marie Aubert (Institut de Mathematique de Jussieu)

Título: Conjectures on representations of p-adic groups in relation
with the local Langlands correspondence

Resumen : We will present several conjectures about complex repre-
sentations of p-adic reductive groups in relation with the local Lang-
lands correspondence.
On the representation side we will consider an arbitrary Bernstein
component in the space of irreducible smooth representations of the p-
adic group and describe a conjectural simple description of it in terms
of a twisted extended quotient of the associated Bernstein torus with
respect to the associated nite group. That is is possible is explained
by the expected shape of the Hecke algebra associated to the Benstein
component. These conjectures have been proved for principal series
representations of split groups, for inner forms of the general linear
group and for inner forms of the special linear group. It is joint work
with Paul Baum, Roger Plymen and Maarten Solleveld.
Next we will describe a Galois analog, due to Ahmed Moussaoui, of
the above description, in which the role of the Bernstein component is
played by a certain subset of the set of enhanced Langlands parame-
ters. It involves in particular a conjectural geometric parametrization
of the supercuspidal representations, which is proved for symplectic
and orthogonal groups.





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