## *Geometric Analysis on Minimal Representations*.
Workshop on
Integral Geometry and Group Representations (organized by Fulton B.
Gonzalez, Tomoyuki Kakehi, Toshiyuki Kobayashi, Toshio Oshima). Tambara
Institute of Mathematical Sciences, the University of Tokyo, Japan, 5-10
August 2009.

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.
We may consider that minimal representations (from the viewpoint of groups)
as ''maximal symmetries (from the viewpoint of representation spaces)'',
and thus propose to use minimal reprn as a guiding principle to find new
interactions with other fields of mathematics.
Highlighting geometric analysis on minimal representations of *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