## *Geometric Analysis on Minimal Representations*.
Colloquium. Université de Reims, France, 5 October 2010.
promised.

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.

© Toshiyuki Kobayashi