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Contractions of group representations via geometric quantisation

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Title: Contractions of group representations via geometric quantisation
Authors: Akylzhanov, R
Arnaudon, A
Item 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.
Issue Date: 9-Feb-2018
URI: http://hdl.handle.net/10044/1/62929
Copyright Statement: © 2018 The Author(s).
Sponsor/Funder: Engineering and Physical Sciences Research Council
Funder's Grant Number: EP/R003025/1
Keywords: math.RT
22D10 (Primary), 53D50 (Secondary)
Notes: This is still working version: comments welcome!
Appears in Collections:Pure Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences
Mathematics