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On the Notion of Conductor in the Local Geometric Langlands Correspondence

  Published:2016-06-02
 Printed: Feb 2017
  • Masoud Kamgarpour,
    School of Mathematics and Physics, The University of Queensland, Australia
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Abstract

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 local geometric Langlands, connections, cyclic vectors, opers, conductors, Segal-Sugawara operators, Chervov-Molev operators, critical level, smooth representations, affine Kac-Moody algebra, categorical representations
MSC Classifications: 17B67, 17B69, 22E50, 20G25 show english descriptions Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
Vertex operators; vertex operator algebras and related structures
Representations of Lie and linear algebraic groups over local fields [See also 20G05]
Linear algebraic groups over local fields and their integers
17B67 - Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
17B69 - Vertex operators; vertex operator algebras and related structures
22E50 - Representations of Lie and linear algebraic groups over local fields [See also 20G05]
20G25 - Linear algebraic groups over local fields and their integers
 

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