Vinberg’s θ-groups and rigid connections

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Abstract

Let G be a simple complex group of adjoint type. In his unpublished work, Z. Yun associated to each θ-group (G0, g1) and a vector X ∈ g1 a flat G-connection ∇X on the trivial G-bundle on P1 −{0, ∞}, generalizing the construction of Frenkel and Gross in [5]. In this paper, we study the local monodromies of the flat G-connection ∇X and compute the de Rham cohomology of ∇X with value in the adjoint representation of G. In particular, we show that in many cases the connection ∇X is cohomologically rigid.

Original languageEnglish (US)
Pages (from-to)7321-7343
Number of pages23
JournalInternational Mathematics Research Notices
Volume2017
Issue number23
DOIs
StatePublished - Dec 1 2017
Externally publishedYes

Bibliographical note

Funding Information:
T.-H.C. was partially supported by an AMS-Simons Travel Grant.

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