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Search: MSC category 17B69 ( Vertex operators; vertex operator algebras and related structures )

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1. CJM Online first

Kamgarpour, Masoud
On the notion of conductor in the local geometric Langlands correspondence
Under the local Langlands correspondence, the conductor of an irreducible representation of $\operatorname{Gl}_n(F)$ is greater than the Swan conductor of the corresponding Galois representation. In this paper, we establish the geometric analogue of this statement by showing that the conductor of a categorical representation of the loop group is greater than the irregularity of the corresponding meromorphic connection.

Keywords:local geometric Langlands, connections, cyclic vectors, opers, conductors, Segal-Sugawara operators, Chervov-Molev operators, critical level, smooth representations, affine Kac-Moody algebra, categorical representations
Categories:17B67, 17B69, 22E50, 20G25

2. CJM 2014 (vol 67 pp. 573)

Chen, Fulin; Gao, Yun; Jing, Naihuan; Tan, Shaobin
Twisted Vertex Operators and Unitary Lie Algebras
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
Categories:17B60, 17B69

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