Representations of GL_2(F) and Equivariant Vector Bundles with Connection on the Drinfeld Upper Half-Plane.

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• James Taylor, University of Oxford
• Wednesday 13 March 2024, 16:30-17:30
• MR12.

If you have a question about this talk, please contact Adam Jones.

If F is a finite extension of Q_p, then the Drinfeld upper half-plane is a certain non-archimedean analogue of the complex upper half plane. This space has a natural action of GL_2(F), and has been shown to be a very fruitful object to study if one is interested in the representation theory of GL_2(F). In this talk, I will introduce this space, and try to motivate why one might be interested in studying equivariant vector bundle with connection on this space in order to better understand locally analytic representations of GL_2(F). I will also explain my current work which classifies exactly which of these equivariant vector bundles with connection arise from the Drinfeld tower, and relates this subcategory to the category of smooth representations of the group of norm one elements in D, the central division algebra over F of dimension 4.

This talk is part of the Algebra and Representation Theory Seminar series.

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