Unitary modules over the gap-$p$ Virasoro algebras

TL;DR

This paper characterizes the conditions under which irreducible Harish-Chandra modules over the gap-$p$ Virasoro algebra are unitary, advancing understanding of their representation theory.

Contribution

It provides a complete criterion for unitarity of modules over the gap-$p$ Virasoro algebra, a novel result in this area.

Findings

Derived explicit unitarity conditions for modules

Classified all unitary irreducible modules over the algebra

Enhanced understanding of the algebra's representation theory

Abstract

For any irreducible Harish-Chandra module $V$ over the gap-$p$ Virasoro algebra, we determine the condition for $V$ to be unitary.