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# Twisted Vertex Operators and Unitary Lie Algebras

Published:2014-04-28
Printed: Jun 2015
• Fulin Chen,
Department of Mathematics, Xiamen University, Xiamen, China 361005
• Yun Gao,
Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3
• Naihuan Jing,
Department of Mathematics, North Carolina State University, Raleigh, NC, USA 27695
• Shaobin Tan,
Department of Mathematics, Xiamen University, Xiamen, China 361005
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## Abstract

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 $A_n^{(2)}$ are recovered by the new method.
 Keywords: Lie algebra, vertex operator, representation theory
 MSC Classifications: 17B60 - Lie (super)algebras associated with other structures (associative, Jordan, etc.) [See also 16W10, 17C40, 17C50] 17B69 - Vertex operators; vertex operator algebras and related structures