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Contractions of group representations via geometric quantisation
File | Description | Size | Format | |
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1802.03348v1.pdf | Working paper | 205.84 kB | Adobe PDF | View/Open |
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 |