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Representations of the Planar Galilean Conformal Algebra

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Abstract

In this paper, the planar Galilean conformal algebra \(\mathcal {G}\) is investigated, which is an infinite-dimensional extension of the finite-dimensional Galilean conformal algebra in \((2+1)\) dimensional space-time. We study simple restricted modules over \(\mathcal {G}\), including the highest weight modules and Whittaker modules. More precisely, we use simple modules over the finite-dimensional solvable Lie algebras to construct many simple restricted modules over \(\mathcal {G}\). Also, we present several equivalent descriptions for simple restricted modules over \(\mathcal {G}\).

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Acknowledgements

The authors would like to thank the referees for valuable suggestions to improve the paper. The first author is partially supported by CSC of China (No. 201906340096), and NSF of China (Grants 11771410, 11931009). The second author is supported by NSERC of Canada and NSFC grant 11931009.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, Anhui, People’s Republic of China

    Dongfang Gao

  2. Department of Mathematics and Statistics, York University, Toronto, ON, M3J 1P3, Canada

    Yun Gao

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  1. Dongfang Gao
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  2. Yun Gao
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Correspondence to Yun Gao.

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Communicated by C. Schweigert.

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Gao, D., Gao, Y. Representations of the Planar Galilean Conformal Algebra. Commun. Math. Phys. 391, 199–221 (2022). https://doi.org/10.1007/s00220-021-04302-9

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