Contractions of group representations via geometric quantisation
Representation Theory
2018-12-18 v2
Abstract
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 into . 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.
Cite
@article{arxiv.1802.03348,
title = {Contractions of group representations via geometric quantisation},
author = {Rauan Akylzhanov and Alexis Arnaudon},
journal= {arXiv preprint arXiv:1802.03348},
year = {2018}
}