Heisenberg Idempotents on Unipotent Groups

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Let G be an algebraic group over an algebraically closed field of positive characteristic such that its neutral connected component is a unipotent group. We consider a certain class of closed idempotents in the braided monoidal category (under convolution of complexes) DG(G) known as Heisenberg idempotents. For such an idempotent e, we will prove certain results about the Hecke subcategory eDG(G) conjectured by V. Drinfeld. In particular, we will see that it is the bounded derived category of a modular category.