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October 20, 2025Open Access

Whittaker modules over the loop Virasoro algebra

Key Points

The study identifies necessary conditions for Whittaker modules over the loop Witt algebra to be simple, enhancing understanding of module theory.
Essential irreducibility criteria are determined for Whittaker modules over the loop Virasoro algebra, with applications to affine Lie algebras.
A family of Whittaker modules is analyzed, revealing insights into their structure and irreducible components for advanced algebraic research.
The findings provide critical criteria for universal Whittaker modules of the affine Lie algebra, paving the way for future studies.

Abstract

In this paper, we first study two classes of Whittaker modules over the loop Witt algebra g: =W, where W=Der (Ct), A=Ct, 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 L: =Vir, 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 sl₂.

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