## *Analysis on Minimal Representations*.
Special Seminar [Mathematics]. IPMU, the University of Tokyo, Japan, 9 December 2010.

Minimal representations are building blocks of unitary representations,
which are the smallest infinite dimensional unitary representations of
reductive groups.
The Weil representation for the metaplectic group, which plays a
prominent role in number theory, is a classic example.
Minimal representations (viewed from groups) have ''maximal symmetries
(viewed from representation spaces)''.
The second viewpoint brings us to a rich study of geometric analysis on
minimal representations. Highlighting minimal representations
of the indefinite orthogonal group *O*(*p*,*q*), I plan to discuss
conservative quantities of ultra-hyperbolic equations, a generalized
Fourier transform for the isotropic cone, and its deformation theory.

© Toshiyuki Kobayashi