The super W_{1+\infty} algebra with integral central charge

Understand

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).