ABSTRACT
A new method of orbits, the deformation program, was introducted by M. Flato and C. Fronsdal [3], [4]. It is based on the use of (formal) deformations of an algebra of functions on the coadjoint orbits, called star products. We present here a deformation program for the semi-simple Lie group G = SU(1, 2). For an orbit O f ; f ∈ G * https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187834/69daaf7f-2564-4f2f-9a9d-3a9774ce28b0/content/eq2011.tif"/> associated to discrete series, we use Berezin’s symbolic calculus to define our star product [7]. By combining these two constructions we have the star exponential on G * https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187834/69daaf7f-2564-4f2f-9a9d-3a9774ce28b0/content/eq2012.tif"/> and the adapted Fourier transform.
