The super W_{1+\infty} algebra with integral central charge
Abstract
The Lie superalgebra SD of regular differential operators on the super circle has a universal central extension \hat{SD}. For each c\in C, the vacuum module M_c(\hat{SD}) of central charge c admits a vertex superalgebra structure, and M_c(\hat{SD}) \cong M_{-c}(\hat{SD}). The irreducible quotient V_c(\hat{SD}) of the vacuum module is known as the super W_{1+\infty} algebra. We show that for each integer n>0, V_n(\hat{SD}) has a minimal strong generating set consisting of 4n fields, and we identify it with a W-algebra associated to the purely odd simple root system of gl(n|n). Finally, we realize V_n(\hat{SD}) as the limit of a family of commutant vertex algebras that generically have the same graded character and possess a minimal strong generating set of the same cardinality.
Cite
@article{arxiv.1209.6032,
title = {The super W_{1+\infty} algebra with integral central charge},
author = {Thomas Creutzig and Andrew R. Linshaw},
journal= {arXiv preprint arXiv:1209.6032},
year = {2021}
}
Comments
A few corrections, final version. arXiv admin note: substantial text overlap with arXiv:1205.4469