Non-weight modules over gap-$p$ Virasoro algebras

TL;DR

This paper investigates non-weight modules over gap-$p$ Virasoro algebras, classifying irreducible modules and establishing conditions for irreducibility of various module types, advancing understanding of their structure.

Contribution

It provides a classification of rank-1 $$-free modules and determines irreducibility conditions for tensor products of modules over gap-$p$ Virasoro algebras.

Findings

Necessary and sufficient conditions for irreducibility of universal Whittaker modules.

Classification of rank-1 $
C$-free modules.

Irreducibility criteria for tensor products of modules.

Abstract

In this paper, we study non-weight modules over gap-$p$ Virasoro algebras, including Whittaker modules, $\mathcal{U}(\mathbb{C} L_0)$-free modules and their tensor products. We establish necessary and sufficient conditions for universal Whittaker modules to be irreducible and study the structure of irreducible Whittaker modules. The $\mathcal{U}(\mathbb{C} L_0)$-free modules of rank 1 are classified and the irreducibility of such modules are determined. Moreover, the irreducibility of tensor products of $\mathcal{U}(\mathbb{C} L_0)$-free modules of rank 1 and irreducible restricted modules is also determined.