## *Analysis on Minimal Representations*.
Geometry, Symmetry and Physics.
Yale University, USA, 26 March 2009.

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 analog of
the Schrödinger model. The latter model leads us to a natural
generalization of the ''Fourier transform'' on the isotropic cone, and an
extension of some earlier work by R. Howe on the oscillator semigroup for
the Weil representation.

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© Toshiyuki Kobayashi