2012/09/30 by Thomas Creutzig, Andrew R. Linshaw
Mathematics · #math.QA #math.RT
paper · pdf · doi:10.1090/s0002-9947-2015-06214-x
published as Trans. Amer. Math. Soc. 367 (2015), 5521-5551 · A few corrections, final version. arXiv admin note: substantial text overlap with arXiv:1205.4469
arxiv created 2013/06/27 · arxiv updated 2021/05/21
The Lie superalgebra SD of regular differential operators on the super circle has a universal central extension SD. For each c∈ C, the vacuum module Mc(SD) of central charge c admits a vertex superalgebra structure, and Mc(SD) ≅ M-c(SD). The irreducible quotient Vc(SD) of the vacuum module is known as the super W1+∞ algebra. We show that for each integer n>0, Vn(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 Vn(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.