The Functors FGP over Local Fields of Positive Characteristic

Let G be a split connected reductive group over a non-archimedean local field. In the p-adic setting, Orlik-Strauch constructed functors from the BGG category O associated to the Lie algebra of G to the category of locally analytic representation of G. We generalize these functors to such groups over non-archimedean local fields of arbitrary characteristic. To this end, we introduce the hyperalgebra of a non-archimedean Lie group G, which generalizes its Lie algebra, and consider topological modules over the algebra of locally analytic distributions on G and subalgebras related to this hyperalgebra.