Analysis on Minimal Representations. Special Seminar [Mathematics]. IPMU, the University of Tokyo, Japan, 9 December 2010.

Minimal representations are building blocks of unitary representations, which are the smallest infinite dimensional unitary representations of reductive groups. 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)''. The second viewpoint brings us to a rich study of geometric analysis on minimal representations. Highlighting minimal representations of the indefinite orthogonal group O(p,q), I plan to discuss conservative quantities of ultra-hyperbolic equations, a generalized Fourier transform for the isotropic cone, and its deformation theory.

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© Toshiyuki Kobayashi