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SUMMARY:Complementary Series for Hyperbolic Groups
DTSTART;VALUE=DATE-TIME:20191209T153000Z
DTEND;VALUE=DATE-TIME:20191209T164500Z
DTSTAMP;VALUE=DATE-TIME:20200224T083117Z
UID:indico-event-5260@indico.math.cnrs.fr
DESCRIPTION:To sum up: We will define complementary series for hyperbolic
groups and prove their irreducibility.\n\nMore precisely: The complementar
y series representations are a family of unitary representations that can
be realized on the Gromov boundary of the hyperbolic group. They can be vi
ewed as a one-parameter deformation of the quasi-regular representation ar
ising on the boundary\, "sometimes" approaching the trivial representation
\, in a certain sense. The starting point of this work is to find a suitab
le scalar product in order to unitarize the complementary series. Then\, a
spectral estimates combined with counting estimates enable us to prove an
ergodic theorem à la Bader-Muchnik to achieve the irreducibility.\n\nJoi
nt work with Kevin Boucher and Jean-Claude Picaud.\n\nhttps://indico.math.
cnrs.fr/event/5260/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/5260/
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