Document Type

Article

Publication Date

10-1-2019

Abstract

Let G be a simple complex algebraic group. We prove that the irregularity of the adjoint connection of an irregular flat G-bundle on the formal punctured disk is always greater than or equal to the rank of G. This can be considered as a geometric analogue of a conjecture of Gross and Reeder. We will also show that the irregular connections with minimum adjoint irregularity are precisely the (formal) Frenkel-Gross connections. As a corollary, we establish the de Rham analogue of a conjecture of Heinloth, Nĝo, and Yun for G = SLn.

Publication Source (Journal or Book title)

American Journal of Mathematics

First Page

1457

Last Page

1476

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