×

Contraction of \(\mathrm{SU}(1,1)\) to the Heisenberg group. (Contraction de \(\mathrm{SU}(1,1)\) vers le groupe de Heisenberg.) (French) Zbl 1074.22005

Travaux mathématiques. Fasc. XV. Luxembourg: Université du Luxembourg, Séminaire de Mathématique (ISBN 2-87971-251-3/pbk). Trav. Math. 15, 19-43 (2004).
Summary: We show that the discrete series representations of \(\mathrm{SU}(1,1)\) can be contracted in the sense of J. Mickelsson and J. Niederle [Commun. Math. Phys. 27, 167–180 (1972; Zbl 0236.22021)] 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 the Lie algebras level is obtained by considering Hamiltonian functions on these coadjoint orbits.
For the entire collection see [Zbl 1065.22001].

MSC:

22E46 Semisimple Lie groups and their representations

Citations:

Zbl 0236.22021