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arXiv · 1812.10662

Conformal mechanical treatment of Calogero-Moser model and infinite dimensional Lie algebra of conformal Galilei type

N. Aizawa·K. Amakawa·S. Doi
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Abstract

We present a relationship between the Calogero-Moser particles confined in harmonic oscillator potentials and a representation theory of the infinite dimensional Lie algebra which is a semi-direct sum of Virasoro algebra and its module. More precisely, it is a correspondence of excited states of the model and singular vectors in Verma modules over the algebra. This is found by a free field realization of the time evolution operator of the model. We investigate the Verma modules and some explicit example of singular vectors are given.

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N. Aizawa, K. Amakawa, S. Doi. 2019-04-01. Conformal mechanical treatment of Calogero-Moser model and infinite dimensional Lie algebra of conformal Galilei type. https://arxiv.org/abs/1812.10662

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