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 R6n.

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© Toshiyuki Kobayashi