Contractions of group representations via geometric quantization

Abstract

We propose a general framework to contract unitary dual of Lie groups via holomorphic quantization of their coadjoint orbits, using geometric quantization. The sufficient condition for the contractibility of a representation is expressed via cocycles on coadjoint orbits. This condition is verified explicitly for the contraction of SU2 into H. We construct two types of contractions that can be implemented on every matrix Lie group with diagonal contraction matrix.