Kamgarpour, Masoud On the notion of conductor in the local geometric Langlands correspondence. (English) Zbl 1433.17032 Can. J. Math. 69, No. 1, 107-129 (2017). 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. Cited in 1 Document 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 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 PDFBibTeX XMLCite \textit{M. Kamgarpour}, Can. J. Math. 69, No. 1, 107--129 (2017; Zbl 1433.17032) Full Text: DOI arXiv