Categorification and Representation Theory in Lie Theory

Dear Colleagues,

This Special Issue, "Categorification and Representation Theory in Lie Theory," seeks to explore the profound and rapidly evolving intersection of these fields. Categorification—the process of replacing set-theoretic concepts with category-theoretic ones—has provided powerful new insights into the structure of representation theory itself. By lifting classical results to a higher categorical level, we uncover deeper layers of structure and connection. This Special Issue aims to bring together cutting-edge research that demonstrates how categorical methods, such as the use of diagrammatic categories, higher representation theory, and geometric approaches, can solve classical problems and reveal new phenomena in Lie theory. We welcome contributions that advance the categorification of quantum groups and their representations, investigate connections to geometry via coherent sheaves and perverse sheaves on flag varieties, and develop new categorical structures that enhance our understanding of Lie algebras, algebraic groups, and related objects. The goal is to showcase the unifying power of categorification as a fundamental language and tool in modern representation theory.

Dr. Linliang Song
Guest Editor

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