Schrödinger model of minimal representations and branching problems. Minimal Representations and Theta Correspondence: In honor of Gordan Savin for his 60th birthday (organized by Wee Teck Gan, Marcela Hanzer, Alberto Minguez, Goran Muic, and Martin Weissman). (online), The Erwin Schrödinger International Institute for Mathematics and Physics (ESI), 11-15 April 2022.

I plan to explain

(a) general theory on the restrictions of ''small representations” to subgroups,
(b) the Schrödinger model of minimal representations of some real reductive groups.

Then using the following guiding hypothesis

small representations (algebra) = large symmetry in function spaces (analysis)

as a guiding principle, I would like to discuss how the ''huge” group symmetries in the minimal representations yield a new direction of global analysis by concrete examples such as a deformation theory of the Fourier transform and some new families of special functions via symmetry breaking.

© Toshiyuki Kobayashi