Contraction de $SU(2)$ vers le groupe de Heisenberg et calcul de Berezin

Benjamin Cahen

Abstract: We show that the unitary irreducible representations of $SU(2)$ can be contracted in the sense of Mickelsson and Niederle [MN] to the unitary irreducible representations of the Heisenberg group by use of Berezin calculus on the coadjoint orbits associated to these representations. An analogous result at Lie algebras level is obtained by considering hamiltonian functions on these coadjoint orbits. In particular we give an easy proof of a result of F. Ricci [R].

[MN] Mickelsson, J.; Niederle, J.: Contractions of Representations of de Sitter Groups. Commun. math. Phys. {\bf 27} (1972), 167--180.

[R] Ricci, F.: A Contraction of $SU(2)$ to the Heisenberg Group. Mh. Math. {\bf 101} (1986), 211--225.

Keywords: Groupes de Lie, représentations, orbites coadjointes, contraction, calcul de Berezin

Classification (MSC2000): 22E46, 53D50, 81R30, 81S10

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