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