Skip to main content

Harmonic analysis on reductive groups

Ziel

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.

Aufforderung zur Vorschlagseinreichung

ERC-2010-AdG_20100224
Andere Projekte für diesen Aufruf anzeigen

Gastgebende Einrichtung

UNIVERSITEIT VAN AMSTERDAM
Adresse
Spui 21
1012WX Amsterdam
Niederlande
Aktivitätstyp
Higher or Secondary Education Establishments
EU-Beitrag
€ 960 017,60
Hauptforscher
Eric Marcus Opdam (Prof.)
Kontakt Verwaltung
J.C.M. Lansbergen (Ms.)

Begünstigte (3)

UNIVERSITEIT VAN AMSTERDAM
Niederlande
EU-Beitrag
€ 960 017,60
Adresse
Spui 21
1012WX Amsterdam
Aktivitätstyp
Higher or Secondary Education Establishments
Hauptforscher
Eric Marcus Opdam (Prof.)
Kontakt Verwaltung
J.C.M. Lansbergen (Ms.)
GOTTFRIED WILHELM LEIBNIZ UNIVERSITAET HANNOVER

Beteiligung beendet

Deutschland
EU-Beitrag
€ 128 480,23
Adresse
Welfengarten 1
30167 Hannover
Aktivitätstyp
Higher or Secondary Education Establishments
Kontakt Verwaltung
Bernhard Kroetz (Prof.)
UNIVERSITAET PADERBORN
Deutschland
EU-Beitrag
€ 680 502,17
Adresse
Warburger Strasse 100
33098 Paderborn
Aktivitätstyp
Higher or Secondary Education Establishments
Kontakt Verwaltung
Daniela Gerdes (Ms.)