Cel 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. Dziedzina nauki natural sciencesmathematicspure mathematicsalgebra Program(-y) 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) Temat(-y) ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations 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 Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Koszt całkowity Brak danych Beneficjenci (3) Sortuj alfabetycznie Sortuj według wkładu UE Rozwiń wszystko Zwiń wszystko UNIVERSITEIT VAN AMSTERDAM Niderlandy Wkład UE € 960 017,60 Adres SPUI 21 1012WX Amsterdam 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 Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Koszt całkowity Brak danych GOTTFRIED WILHELM LEIBNIZ UNIVERSITAET HANNOVER Zakończenie uczestnictwa Niemcy Wkład UE € 128 480,23 Adres WELFENGARTEN 1 30167 Hannover Zobacz na mapie Region Niedersachsen Hannover Region Hannover Rodzaj działalności Higher or Secondary Education Establishments Kontakt administracyjny Bernhard Kroetz (Prof.) Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Koszt całkowity Brak danych UNIVERSITAET PADERBORN Niemcy Wkład UE € 680 502,17 Adres WARBURGER STRASSE 100 33098 Paderborn Zobacz na mapie Region Nordrhein-Westfalen Detmold Paderborn Rodzaj działalności Higher or Secondary Education Establishments Kontakt administracyjny Daniela Gerdes (Ms.) Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Koszt całkowity Brak danych