Combinatorics of monoidal actions in Lie-algebraic context

2025/09/01 by Mazorchuk, Volodymyr, Zhu, Xiaoyu
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2509.01404

Abstract

This paper is, essentially, a survey related to the problem of understanding the combinatorics of the action of the monoidal category of finite dimensional modules over a simple finite dimensional Lie algebra on various categories of Lie algebra modules. A special attention is payed to the Lie algebras \mathfraksl₂ and \mathfraksl₃. A few new general results are collected at the end.

Citations

• Combinatorics of infinite rank module categories over finite dimensional \mathfraksl₃-modules in Lie-algebraic context
• Applying projective functors to arbitrary holonomic simple modules
• Translated simple modules for Lie algebras and simple supermodules for Lie superalgebras
• Simple transitive 2-representations of small quotients of Soergel\n bimodules
• On wild Lie algebras
• La correspondance de McKay

Related

• Combinatorics of infinite rank module categories over finite dimensional \mathfraksl₃-modules in Lie-algebraic context
• Infinite rank module categories over finite dimensional \mathfraksl₂-modules in Lie-algebraic context
• A Note on the categorification of Lie algebras
• Combinatorial representation theory of Lie algebras. Richard Stanley's work and the way it was continued
• Some combinatorial coincidences for standard representations of affine\n Lie algebras