New Quiver-Like Varieties and Lie Superalgebras

In order to extend the geometrization of Yangian R-matrices from Lie algebras $$ \mathfrak {gl}(n) superalgebras $$\mathfrak {gl}(M|N)$$ , we introduce new quiver-related varieties which are associated with representations {gl}(M|N) . define them similarly Nakajima-Cherkis varieties, reformulate construction latter by replacing Hamiltonian reduction intersection generalized Lagrangian subvarieties in cotangent bundles sitting at vertices quiver. The come some their Legendre transforms. We present superalgebra versions stable envelopes for quiver-like that generalize bundle a Grassmannian. generalizations Tarasov–Varchenko weight functions, and show they represent super envelopes. Both functions transform according $$\check{R}$$ -matrices $$M+N=2$$