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UID:4652@test.i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20170222T140000
DTEND;TZID=Europe/Paris:20170222T150000
DTSTAMP:20170207T130000Z
URL:https://test.i2m.univ-amu.fr/events/distributions-on-p-adic-groups-fin
ite-under-the-action-of-the-bernstein-center/
SUMMARY:Distributions on p-adic groups\, finite under the action of the Ber
nstein center -
DESCRIPTION:For a real reductive group G\, the center z(U(g)) of the univer
sal enveloping algebra of the Lie algebra g of G acts on the space of dist
ributions on G. This action proved to be very useful.Over non-Archimedean
local fields\, one can replace this action by the action of the Bernstein
center z of G\, i.e. the center of the category of smooth representations.
However\, this action is not well studied. In my talk I will provide some
tools to work with this action and discuss the following results.1) The w
ave-front set of any z-finite distribution on G over any point x∈G lies
inside the nilpotent cone of $T^∗_xG≅g$.2) Let $H_1\,H_2$⊂G be symme
tric subgroups. Consider the space J of $H_1×H_2$-invariant distributions
on G. We prove that the z-finite distributions in J form a dense subspace
. 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 repla
ced by semi-invariance. Further we apply those results to density and regu
larity of spherical characters.The first result can be viewed as a version
of Howe's expansion of characters. The second result can be viewed as a s
pherical space analog of a classical theorem on density of characters of a
dmissible representations. It can also be viewed as a spectral version of
Bernstein's localization principle.In the Archimedean case\, the first res
ult is well-known and the second remains open.I will also describe an appl
ication of these results to the non-vanishing of certain spherical Bessel
functions. http://www.wisdom.weizmann.ac.il/~dimagur/
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DTSTART:20161030T020000
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