## *1. Conformal Geometry and Schrödinger Model of Minimal
Representations; 2. Generalized Bernstein-Reznikov Integrals* (2 lectures).
Representation Theory
XI. Dubrovnik, Croatia, 14-21 June 2009.

1. Minimal representations are the ''smallest'' infinite dimensional
unitary representations. The Weil representation, which plays a prominent
role in number theory, is a classic example. Most of these are isolated
among the set of all unitary representations, and cannot be built up by
induction.
Highlighting indefinite orthogonal groups, I plan to discuss two models of
minimal representations, namely, the one is the conformal geometric
construction by using the Yamabe operator, and the other is an analogue of
the Schrodinger model. The latter model leads us to a natural
generalization of the ''Fourier transform'' on the isotropic cone.
2. I plan to talk an explicit formula for the integral of a triple
product of powers of sympletc forms on the triple product of spheres in **R**^{6n}.

© Toshiyuki Kobayashi