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

doi:10.1007/s11464-015-0466-y

Front. Math. China

2015, Vol. 10

Issue (5) : 1233-1242 https://doi.org/10.1007/s11464-015-0466-y

RESEARCH ARTICLE

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

Xiufu ZHANG(

)

School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China

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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

Corresponding Author(s): Xiufu ZHANG

Issue Date: 24 June 2015

Cite this article:

Xiufu ZHANG. Classification of simple weight modules for super-Virasoro algebra with a finite-dimensional weight space[J]. Front. Math. China, 2015, 10(5): 1233-1242.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-015-0466-y
https://academic.hep.com.cn/fmc/EN/Y2015/V10/I5/1233

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