Duality in the Category of Andersen-Jantzen-Soergel

TL;DR

This paper explores the duality properties within a specific category introduced by Andersen, Jantzen, and Soergel, which models representations of quantum groups at roots of unity and Lie algebras in positive characteristic.

Contribution

It provides a detailed analysis of how duality operates in the Andersen-Jantzen-Soergel category, enhancing understanding of its structure and representation theory.

Findings

Duality behavior characterized in the category.

Connections established between quantum group and Lie algebra representations.

Structural properties of the category clarified.

Abstract

In the early 1990's Andersen, Jantzen and Soergel introduced a category in order to give a combinatorial model for certain representations of quantum groups at a root of unity and simultaneously of Lie algebras of semisimple algebraic groups in positive characteristic. We will describe the behaviour of duality in this category.