Classification of irreducible Harish-Chandra modules over map full toroidal Lie algebras

2025/08/15 by Mukherjee, Sudipta
#17B66 #17B67 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2508.11448

Abstract

A natural higher dimensional analogue of the affine-Virasoro algebra is the full toroidal Lie algebra. In this paper, we classify irreducible Harish-Chandra modules for map full toroidal Lie algebras. We show that every such module is either a cuspidal or a highest weight module. Furthermore, we prove that they turn out to be single point evaluation modules.

Citations

• Integrable Modules of Map full Toroidal Lie Algebras
• Classification of irreducible Harish-Chandra modules over full toroidal Lie algebras and higher-dimensional Virasoro algebras
• Classification of level zero irreducible integrable modules for twisted full toroidal Lie algebras
• Integrable modules for loop affine-Virasoro algebra
• Supports of weight modules over Witt algebras
• A category of modules for the full toroidal Lie algebra
• Weight modules over exp-polynomial Lie algebras
• Classification of Irreducible integrable modules for toroidal Lie-algebras with finite dimensional weight spaces
• An Extension of the KdV Hierarchy Arising from a Representation of a Toroidal Lie Algebra

Related

• Classification of irreducible Harish-Chandra modules over full toroidal Lie algebras and higher-dimensional Virasoro algebras
• Classification of Harish-Chandra modules over some Lie algebras related to the Virasoro algebra
• Integrable Modules of Map full Toroidal Lie Algebras
• Irreducible modules for map Heisenberg-Virasoro Lie algebras
• Classification of Irreducible Weight Modules with a Finite-dimensional Weight Space over the Twisted Schrödinger-Virasoro Lie algebra