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On the Notion of Conductor in the Local Geometric Langlands Correspondence

Published online by Cambridge University Press:  20 November 2018

Masoud Kamgarpour
Masoud Kamgarpour*
Affiliation:
School of Mathematics and Physics, The University of Queensland, Australia e-mail: masoud@uq.edu.au
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Abstract

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Under the local Langlands correspondence, the conductor of an irreducible representation of $\text{G}{{\text{l}}_{n}}\left( F \right)$ 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

17B6717B6922E5020G25local geometric Langlandsconnectionscyclic vectorsopersconductorsSegal- Sugawara operatorsChervov-Molev operatorscritical levelsmooth representationsaffine Kac-Moody algebracategorical representations
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 69 , Issue 1 , 01 February 2017 , pp. 107 - 129
Copyright
Copyright © Canadian Mathematical Society 2017

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