## *Geometric Analysis on Minimal Representations*.
Geometry and Dynamics Seminar. Université Lille, France, 6 January
2011.

Minimal representations are the smallest infinite dimensional
unitary representations. The Weil representation for the metaplectic group,
which plays a prominent role in number theory, is a classic example.
Our viewpoint of minimal representations is that they shoud have ''maximal
symmetries'' on representation spaces. We then initiate a new line of
investigations to use minimal representations as a guiding principle to
find interactions with other fields of mathematics.
Highlighting geometric analysis on minimal representations of generalized
Lorentz group *O*(*p*,*q*), I plan to discuss conservative quantities of
ultrahyperbolic equations, the generalization of the Fourier-Hankel
transform on the *L*^{2}-model, and its deformation.

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© Toshiyuki Kobayashi