Whittaker modules over the loop Virasoro algebra

2025/09/29 by Zhiqiang Li, Li, Zhiqiang, Shaobin Tan +3
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2509.24574

openalex publication_date 2025/09/29 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

In this paper, we first study two classes of Whittaker modules over the loop Witt algebra \mathfrak g:=W\otimesA, where W=Der(ℂ[t]), A=ℂ[t,t^-1]. The necessary and sufficient conditions for these Whittaker modules being simple are determined. Furthermore, we study a family of Whittaker modules over the loop Virasoro algebra \mathfrakL:=Vir\otimesA, where Vir is the Virasoro algebra. The irreducibility criterion for these Whittaker modules are obtained. As an application, we give the irreducibility criterion for universal Whittaker modules of the affine Lie algebra \widehat\mathfraksl₂.

Citations

• Simple modules for untwisted affine Lie algebras induced from nilpotent loop subalgebras
• Blocks and modules for Whittaker pairs
• Whittaker Modules for the Virasoro Algebra
• Whittaker Modules for Generalized Weyl Algebras
• Weight modules over exp-polynomial Lie algebras
• Quantum deformation of Whittaker modules and Toda lattice

Related

• Whittaker Modules for the Virasoro Algebra
• Whittaker modules for the Schrödinger-Virasoro algebra
• Whittaker categories for the Virasoro algebra
• Whittaker modules for the super-Virasoro algebras
• Whittaker Modules For The W-algebra W(2,2)