Contractions of group representations via geometric quantisation

Rauan Akylzhanov; Alexis Arnaudon

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arXiv · 1802.03348

Contractions of group representations via geometric quantisation

Rauan Akylzhanov·Alexis Arnaudon

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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.

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BibTeX RIS

Rauan Akylzhanov, Alexis Arnaudon. 2018-02-09. Contractions of group representations via geometric quantisation. https://arxiv.org/abs/1802.03348

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