W-(super)algebras have generated great interest in recent years due to their numerous applications in mathematics and physics. The process of Hamiltonian reduction in stages suggests that W-(super)algebras often arise as extensions of tensor products basic building blocks. In type A, we expect that the building blocks are the Gaiotto-Rapcak Y-algebras which arise as 1-parameter quotients of the universal 2-parameter VOA of type W(2,3,…). For types B, C, and D, the quotients of the universal 2-parameter VOA of type W(2,4,…) provide some, but not all, of the necessary building blocks. In this talk we discuss a new universal 2-parameter VOA of type W(1^3,2,3^3,4,…), whose 1-parameter quotients are expected to account for the missing building blocks for W-(super)algebras of types B, C, and D. There are 8 infinite families of such quotients, which are analogues of the Gaiotto-Rapcak Y-algebras. We will explain the process behind the construction of this universal two-parameter VOA and discuss several applications. This is a join work with Thomas Creutzig and Andrew Linshaw.
