Modular representation of Reductive Lie algebras and related combinatorial category

TL;DR

This paper introduces a new combinatorial category related to the representations of reduced enveloping algebras of reductive Lie algebras, connecting it to existing categories used in studying algebraic group characters.

Contribution

It defines and analyzes a novel combinatorial category that aligns with the AJS category, advancing understanding of representations in reductive Lie algebra theory.

Findings

Established compatibility with AJS category

Provided new insights into representations of reduced enveloping algebras

Potential implications for Lusztig's conjecture

Abstract

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.