Classification of simple weight modules for super-Virasoro algebra with a finite-dimensional weight space

Abstract

There are two extensions of Virasoro algebra with particular importance in superstring theory: the Ramond algebra and the Neveu-Schwarz algebra, which are Z₂-graded extensions of the Virasoro algebra. In this paper, we show that the support of a simple weight module over the Ramond algebra with an infinite-dimensional weight space coincides with the weight lattice and that all intersections of non-trivial weight spaces and odd part or even part of the module are infinite-dimensional. This result together with the one that we have obtained over the Neveu-Schwarz algebra generalizes the result for the Virasoro algebra to the super-Virasoro algebras.

Keywords

Super-Virasoro algebra / Ramond algebra / weight module / Harish-Chandra module

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2014 Higher Education Press and Springer-Verlag Berlin Heidelberg