Contractions of group representations via geometric quantisation
File(s)
Working paper
Author(s)
Akylzhanov, Rauan
Arnaudon, Alexis
Type
Working Paper
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 ${\mathrm SU}_2$ 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.
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.
Date Issued
2018-02-09
Citation
2018
Copyright Statement
© 2018 The Author(s).
Sponsor
Engineering and Physical Sciences Research Council
Identifier
http://arxiv.org/abs/1802.03348v1
Grant Number
EP/R003025/1
Subjects
math.RT
math.RT
22D10 (Primary), 53D50 (Secondary)
Notes
This is still working version: comments welcome!