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Twisted Vertex Operators and Unitary Lie Algebras

Published online by Cambridge University Press:  20 November 2018

Fulin Chen
Affiliation:
Department of Mathematics, Xiamen University, Xiamen, China 361005. e-mail: fulinchen@amss.ac.cn, tans@xmu.edu.cn
Yun Gao
Affiliation:
Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3. e-mail: , ygao@yorku.ca
Naihuan Jing
Affiliation:
Department of Mathematics, North Carolina State University, Raleigh, NC, USA 27695. jing@math.ncsu.edu
Shaobin Tan
Affiliation:
Department of Mathematics, Xiamen University, Xiamen, China 361005. e-mail: fulinchen@amss.ac.cn, tans@xmu.edu.cn
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Abstract

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A representation of the central extension of the unitary Lie algebra coordinated with a skew Laurent polynomial ring is constructed using vertex operators over an integral ${{\mathbb{Z}}_{2}}$-lattice. The irreducible decomposition of the representation is explicitly computed and described. As a by-product, some fundamental representations of affine Kac–Moody Lie algebra of type $A_{n}^{\left( 2 \right)}$ are recovered by the new method.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2015

References

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