## *Geometric Analysis on Minimal Representations*.
Geometry and Quantum
Theory. Nijmegen, the Netherlands, 28 June-2 July 2010.

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.
Minimal representations (viewed from groups) have ''maximal symmetries
(viewed from 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.

[

lecture video ]

© Toshiyuki Kobayashi