On equivariant holomorphic differential operators starting from vector-valued cases (Analytic and arithmetic aspects of automorphic representations)

Abstract

The theory of Rankin-Cohen bilinear holomorphic differential operators is well explored for scalar-valued cases, mainly by the work of Ibukiyama. Not so much is known when we start from vector-valued automorphy factors. We will describe some constructions starting from nonholomorphic operators of Maaβ-Shimura type. We focus on operators of order one, but by some compatibility with tensor products we can cover more general situations. For the case of symmetric tensor representations we can however give quite complete results by a direct approach. Some parts of the presentation are based on the Mannheim PhD-thesis 2021 by Julia Meister.