Equivariant Vector Bundles with Connection on Drinfeld Symmetric Spaces

2024/06/20 by James G. Taylor, Taylor, James · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Differential Geometry Research #FOS: Mathematics #Nonlinear Waves and Solitons #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2406.14543

openalex publication_date 2024/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a finite extension F of ℚ_p and n ≥ 1, let D be the division algebra over F of invariant 1/n and let G⁰ be the subgroup of GL_n(F) of elements with norm 1 determinant. We show that the action of D^× on the Drinfeld tower induces an equivalence of categories from finite dimensional smooth representations of D^× to G⁰-finite GL_n(F)-equivariant vector bundles with connection on Ω, the (n-1)-dimensional Drinfeld symmetric space.

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• Character Theory for Semilinear Representations

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