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UID:1593@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20170222T140000
DTEND;TZID=Europe/Paris:20170222T150000
DTSTAMP:20170207T130000Z
URL:https://www.i2m.univ-amu.fr/evenements/distributions-on-p-adic-groups-
 finite-under-the-action-of-the-bernstein-center/
SUMMARY: (...): Distributions on p-adic groups\, finite under the action of
  the Bernstein center 
DESCRIPTION:: For a real reductive group G\, the center z(U(g)) of the univ
 ersal enveloping algebra of the Lie algebra g of G acts on the space of di
 stributions on G. This action proved to be very useful.Over non-Archimedea
 n local fields\, one can replace this action by the action of the Bernstei
 n center z of G\, i.e. the center of the category of smooth representation
 s. However\, this action is not well studied. In my talk I will provide so
 me tools to work with this action and discuss the following results.1) The
  wave-front set of any z-finite distribution on G over any point x∈G lie
 s inside the nilpotent cone of $T^∗_xG≅g$.2) Let $H_1\,H_2$⊂G be sym
 metric subgroups. Consider the space J of $H_1×H_2$-invariant distributio
 ns on G. We prove that the z-finite distributions in J form a dense subspa
 ce. In fact we prove this result in wider generality\, where the groups H_
 i are spherical groups of certain type and the invariance condition is rep
 laced by semi-invariance. Further we apply those results to density and re
 gularity of spherical characters.The first result can be viewed as a versi
 on of Howe's expansion of characters. The second result can be viewed as a
  spherical space analog of a classical theorem on density of characters of
  admissible representations. It can also be viewed as a spectral version o
 f Bernstein's localization principle.In the Archimedean case\, the first r
 esult is well-known and the second remains open.I will also describe an ap
 plication of these results to the non-vanishing of certain spherical Besse
 l functions. http://www.wisdom.weizmann.ac.il/~dimagur/
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