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UID:7981@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20151103T140000
DTEND;TZID=Europe/Paris:20151103T150000
DTSTAMP:20241120T205619Z
URL:https://www.i2m.univ-amu.fr/evenements/on-the-spherical-automorphic-sp
 ectrum-of-a-split-reductive-group/
SUMMARY: (...): On the spherical automorphic spectrum of a split reductive 
 group
DESCRIPTION:: Let G be connected reductive group over a number field F and 
 let A denote the ring of adèles of F.Langlands gave a decomposition of th
 e space of square-integrable functions on the quotient G(F)\\G(A) (modulo 
 the center) as a direct sum in terms of equivalence classes of cuspidal da
 ta. Assume G is split and let K be a maximal compact subgroup of G(A) with
  factors in each finite place equal to a hyperspecial maximal compact subg
 roup. The summand corresponding to the cuspidal datum (T\,1)\, where T is 
 a maximal split torus and 1 the trivial character of T(F)\\T(A)\, contains
  a non-empty subspace consisting of K-fixed vectors. It was described by s
 everal authors in many special cases. In a joint work with E. Opdam and V.
  Heiermann\, we provide a uniform description of this space of K-fixed vec
 tors which holds for every split reductive group over F.http://www.uva.nl/
 en/contact/staff/item/m.goncalvesdemartino.html?f=MARTINO
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