The Euclidean Fourier transform appears as the ''inversion unitary operator'' of the Weil representation realized in the the Schroedinger model, which is a minimal representation of a simple group of type C.
I plan to discuss a ''generalized Fourier transform'' arising from a minimal representation of a simple group of type D ().
Deformation theory () will be also discussed.
 to appear in Memoirs of Amer Math Soc (with G. Mano) .
 C. R. Math. Acad. Sci. Paris, 347:1119-1124, 2009 (with S. Ben Saïd and B. Ørsted). Full paper is available at arXiv:0907.3749.
© Toshiyuki Kobayashi