## *Geometric Analysis on Minimal Representations*.
Representation
Theory of Real Reductive Groups (organized by Jeffrey Adams,
Susana Salamanca, John Stembridge, Peter Trapa and David Vogan). University of Utah, Salt Lake City, USA,
27-31 July 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.

[ lecturenotes ]

© Toshiyuki Kobayashi