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Harmonic analysis on reductive groups

Cel

We propose to attack a variety of fundamental open problems in
harmonic analysis on $p$-adic and real reductive groups.

Specifically we seek solutions to the local Langlands conjectures
and various normalization problems of discrete series representations.
For $p$-adic groups, affine Hecke algebras are a major technical tool.
Our understanding of these algebras with unequal parameters has
advanced recently and allows us to address these problems.
We will compute the Plancherel measure on the Bernstein components
explicitly. Using a new transfer principle of Plancherel measures
between Hecke algebras we will combine Bernstein components to form
$L$-packets, following earlier work of Reeder in small rank.
We start with the tamely ramified case, building on work of
Reeder-Debacker. We will also explore these methods for $L$-packets
of positive depth, using recent progress due to Yu and others.
Furthermore we intend to study non-tempered
unitary representations via affine Hecke algebras, extending the
work of Barbasch-Moy on the Iwahori spherical unitary dual.

As for real reductive groups we intend to address essential
questions on the convergence of the Fourier-transform. This theory
is widely developed for functions which transform finitely under a
maximal compact subgroup. We wish to drop this condition in order
to obtain global final statements for various classes of rapidly
decreasing functions. We intend to extend our results to certain types of
homogeneous spaces, e.g symmetric and multiplicity one spaces. For doing
so we will embark to develop a suitable spherical character theory for
discrete series representations and solve the corresponding normalization
problems.

The analytic nature of the Plancherel measure and the correct interpretation
thereof is the underlying theme which connects the various parts of
this proposal.

Zaproszenie do składania wniosków

ERC-2010-AdG_20100224
Zobacz inne projekty w ramach tego zaproszenia

System finansowania

ERC-AG - ERC Advanced Grant

Instytucja przyjmująca

UNIVERSITEIT VAN AMSTERDAM
Wkład UE
€ 960 017,60
Adres
SPUI 21
1012WX Amsterdam
Niderlandy

Zobacz na mapie

Region
West-Nederland Noord-Holland Groot-Amsterdam
Rodzaj działalności
Higher or Secondary Education Establishments
Kierownik naukowy
Eric Marcus Opdam (Prof.)
Kontakt administracyjny
J.C.M. Lansbergen (Ms.)
Linki
Koszt całkowity
Brak danych

Beneficjenci (3)