  We propose a general framework to contract unitary dual of Lie groups via
holomorphic quantization of their co-adjoint orbits. The sufficient condition
for the contractability of a representation is expressed via cocycles on
coadjoint orbits. This condition is checked explicitly for the contraction of
${\mathrm SU}_2$ into $\mathbb{H}$. The main tool is the geometric
quantization. We construct two types of contractions that can be implemented on
every matrix Lie group with diagonal contraction matrix.
