Objetivo We propose to attack a variety of fundamental open problems inharmonic analysis on $p$-adic and real reductive groups.Specifically we seek solutions to the local Langlands conjecturesand 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 hasadvanced recently and allows us to address these problems.We will compute the Plancherel measure on the Bernstein componentsexplicitly. Using a new transfer principle of Plancherel measuresbetween 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 ofReeder-Debacker. We will also explore these methods for $L$-packetsof positive depth, using recent progress due to Yu and others.Furthermore we intend to study non-temperedunitary representations via affine Hecke algebras, extending thework of Barbasch-Moy on the Iwahori spherical unitary dual.As for real reductive groups we intend to address essentialquestions on the convergence of the Fourier-transform. This theoryis widely developed for functions which transform finitely under amaximal compact subgroup. We wish to drop this condition in orderto obtain global final statements for various classes of rapidlydecreasing functions. We intend to extend our results to certain types ofhomogeneous spaces, e.g symmetric and multiplicity one spaces. For doingso we will embark to develop a suitable spherical character theory fordiscrete series representations and solve the corresponding normalizationproblems.The analytic nature of the Plancherel measure and the correct interpretationthereof is the underlying theme which connects the various parts ofthis proposal. Ámbito científico natural sciencesmathematicspure mathematicsalgebra Programa(s) 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) Tema(s) ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations Convocatoria de propuestas ERC-2010-AdG_20100224 Consulte otros proyectos de esta convocatoria Régimen de financiación ERC-AG - ERC Advanced Grant Institución de acogida UNIVERSITEIT VAN AMSTERDAM Aportación de la UE € 960 017,60 Dirección SPUI 21 1012WX Amsterdam Países Bajos Ver en el mapa Región West-Nederland Noord-Holland Groot-Amsterdam Tipo de actividad Higher or Secondary Education Establishments Investigador principal Eric Marcus Opdam (Prof.) Contacto administrativo J.C.M. Lansbergen (Ms.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos Beneficiarios (3) Ordenar alfabéticamente Ordenar por aportación de la UE Ampliar todo Contraer todo UNIVERSITEIT VAN AMSTERDAM Países Bajos Aportación de la UE € 960 017,60 Dirección SPUI 21 1012WX Amsterdam Ver en el mapa Región West-Nederland Noord-Holland Groot-Amsterdam Tipo de actividad Higher or Secondary Education Establishments Investigador principal Eric Marcus Opdam (Prof.) Contacto administrativo J.C.M. Lansbergen (Ms.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos GOTTFRIED WILHELM LEIBNIZ UNIVERSITAET HANNOVER La participación finalizó Alemania Aportación de la UE € 128 480,23 Dirección WELFENGARTEN 1 30167 Hannover Ver en el mapa Región Niedersachsen Hannover Region Hannover Tipo de actividad Higher or Secondary Education Establishments Contacto administrativo Bernhard Kroetz (Prof.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos UNIVERSITAET PADERBORN Alemania Aportación de la UE € 680 502,17 Dirección WARBURGER STRASSE 100 33098 Paderborn Ver en el mapa Región Nordrhein-Westfalen Detmold Paderborn Tipo de actividad Higher or Secondary Education Establishments Contacto administrativo Daniela Gerdes (Ms.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos