The higher Verlinde categories Ver_{p^n} were introduced independently by Coulembier and Benson-Etingof-Ostrik as generalizations of Ver_p (the semisimplification of Rep(Z/pZ)); they conjectured that these categories appear in the analog of Deligne’s theorem in positive characteristic, i.e. every symmetric tensor category of moderate growth admits a fiber functor to the union Ver_{p^\infty} of the nested sequence Ver_p \subset Ver_{p^2} \subset.... Therefore, studying representations of affine group schemes in symmetric tensor categories of moderate growth reduces to studying representations of group schemes in these higher Verlinde categories. In this talk, we consider representation theory in Ver_4^+, which has a concrete description as the representation category Rep(k[d]/d^2) with twisted braiding. We present some results on representations of general linear groups, related group schemes, and Lie algebras in Ver_4^+, and discuss unanswered questions in this area.