location:  Publications → journals → CJM
Abstract view

# 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
 Format: LaTeX MathJax PDF

## 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
 MSC Classifications: 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

 top of page | contact us | privacy | site map |