Twisted Vertex Operators and Unitary Lie Algebras

Chen, Fulin ; Gao, Yun ; Jing, Naihuan ; Tan, Shaobin

Canadian journal of mathematics, Tome 67 (2015) no. 3, pp. 573-596

Résumé

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.

Détail

DOI : 10.4153/CJM-2014-010-1

Mots-clés : 17B60, 17B69, Lie algebra, vertex operator, representation theory

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