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On the notion of conductor in the local geometric Langlands correspondence. (English) Zbl 1433.17032

Summary: Under the local Langlands correspondence, the conductor of an irreducible representation of \(\mathrm{GL}_n(F)\) 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.

MSC:

17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
17B69 Vertex operators; vertex operator algebras and related structures
22E57 Geometric Langlands program: representation-theoretic aspects
20G25 Linear algebraic groups over local fields and their integers
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