Equivariant Vector Bundles with Connection on Drinfeld Symmetric Spaces

Paper

Abstract

For a finite extension

and

, let

be the division algebra over

of invariant

and let

be the subgroup of

of elements with norm

determinant. We show that the action of

on the Drinfeld tower induces an equivalence of categories from finite dimensional smooth representations of

-finite

-equivariant vector bundles with connection on

, the

-dimensional Drinfeld symmetric space.