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 L2-model, and its deformation.

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© Toshiyuki Kobayashi