On the structure of Verma module over Virasoro and Neveu-Schwarz algebras

TL;DR

This paper offers a simplified proof of the structure of Verma modules over the Virasoro algebra and presents new results on the Neveu-Schwarz algebra, enhancing understanding of their module structures.

Contribution

It provides a simpler proof for Virasoro Verma modules and extends structural results to certain Neveu-Schwarz Verma modules, with potential for broader generalization.

Findings

Simplified proof for Virasoro Verma modules

New structural results for Neveu-Schwarz Verma modules

Potential for generalizing to broader classes of Neveu-Schwarz modules

Abstract

In the paper we present a different proof of the theorem of B. L. Feigin and D. B. Fuchs about the structure of Verma modules over Virasoro algebra. We state some new results about the structure of Verma modules over Neveu-Schwarz. The proof has thwo advantages: first, it is simplier in the most interesting cases (for example in the so called minimal models), second, it can be generalized for Neveu-Schwarz algebra for some class of Verma modules.