Stratonovich-Weyl correspondence for the real diamond group
Received: 27 September 2012
Accepted in revised form: 3 June 2013
Mathematics Subject Classification (2010): 22E27, 22E25, 81S10, 81R30.
Keywords: Stratonovich-Weyl correspondence; Berezin quantization; diamond group; coherent states; coadjoint orbit; unitary representation; holomorphic representation; Schrödinger representation; Bargmann-Fock representation; Segal-Bargmann transform.
Abstract: We show that the usual Weyl quantization provides a Stratonovich-Weyl correspondence for the Schrödinger realization of a generic representation of the real diamond group . This Stratonovich-Weyl correspondence is related to that obtained by polarization of the Berezin map in [B. Cahen, Berezin quantization and holomorphic representations, Rend. Sem. Mat. Univ. Padova 129 (2013), 277-297].