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 fucntion 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 transofrm and some new families of special functions via symmetry breaking.