Higher spin sl2 R-matrix from equivariant (co)homology

Abstract

We compute the rational sl2R-matrix acting in the product of two spin-ℓ2 (ℓ∈ N) representations, using a method analogous to the one of Maulik and Okounkov, i.e., by studying the equivariant (co)homology of certain algebraic varieties. These varieties, first considered by Nekrasov and Shatashvili, are typically singular. They may be thought of as the higher spin generalizations of A1 Nakajima quiver varieties (i.e., cotangent bundles of Grassmannians), the latter corresponding to ℓ= 1.