Modular representation of Reductive Lie algebras and related combinatorial category

We introduce and study a combinatorial" category related to the representations of reduced enveloping algebras of reductive Lie algebras in standard Levi form". It is compatible with the so-called AJS category in \cite{AJS94}, where AJS category is an important role in studying the Lusztig’s conjecture on characters of irreducible modules of algebraic group.