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.[ lecture video ]
Minimal representations (viewed from groups) have ''maximal symmetries (viewed from representation spaces)''. We then initiate a new line of investigations to use minimal representations as a guiding principle to find interactions with other fields of mathematics.
Highlighting geometric analysis on minimal representations of generalized Lorentz group 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.
© Toshiyuki Kobayashi