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HARG

Harmonic analysis on reductive groups

Coordinatore	UNIVERSITEIT VAN AMSTERDAM Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie.
Nazionalità Coordinatore	Netherlands [NL]
Totale costo	1˙769˙000 €
EC contributo	1˙769˙000 €
Programma	FP7-IDEAS-ERC Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
Code Call	ERC-2010-AdG_20100224
Funding Scheme	ERC-AG
Anno di inizio	2011
Periodo (anno-mese-giorno)	2011-03-01 - 2016-02-29

Partecipanti

#	participant	country	role	EC contrib. [€]
1	UNIVERSITAET PADERBORN Organization address address: WARBURGER STRASSE 100 city: PADERBORN postcode: 33098 contact info Titolo: Ms. Nome: Daniela Cognome: Gerdes Email: send email Telefono: +49 5251 60 2562	DE (PADERBORN)	beneficiary	680˙502.20
2	GOTTFRIED WILHELM LEIBNIZ UNIVERSITAET HANNOVER Organization address address: Welfengarten 1 city: HANNOVER postcode: 30167 contact info Titolo: Prof. Nome: Bernhard Cognome: Kroetz Email: send email Telefono: +49 511 762 2361 Fax: +49 511762 3518	DE (HANNOVER)	beneficiary	128˙480.23
3	UNIVERSITEIT VAN AMSTERDAM Organization address address: SPUI 21 city: AMSTERDAM postcode: 1012WX contact info Titolo: Ms. Nome: J.C.M. Cognome: Lansbergen Email: send email Telefono: +31 20 5256915 Fax: +31 20 5257675	NL (AMSTERDAM)	hostInstitution	960˙017.60
4	UNIVERSITEIT VAN AMSTERDAM Organization address address: SPUI 21 city: AMSTERDAM postcode: 1012WX contact info Titolo: Prof. Nome: Eric Marcus Cognome: Opdam Email: send email Telefono: 31205255205 Fax: 31205257820	NL (AMSTERDAM)	hostInstitution	960˙017.60

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packets representations functions we theory spaces real p hecke adic discrete plancherel normalization spherical components unitary of transform l for series groups affine reductive algebras bernstein intend reeder

Obiettivo del progetto (Objective)

'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.'