2019/04/30 by Dmitri Bykov, Paul Zinn-Justin
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic number #Algebraic structures and combinatorial models #Complex system #Cotangent bundle #Equivariant map #Homotopy and Cohomology in Algebraic Topology #Product (mathematics) #Quiver #Spin (aerodynamics) #Type (biology) #hep-th #math-ph #math.MP
paper · pdf · doi:10.1007/s11005-020-01302-z
published as Lett. Math. Phys. 110, 2435-2470 (2020)
openalex created_date 2019/05/03 · arxiv created 2020/04/04 · openalex publication_date 2020/06/29 · arxiv updated 2020/10/01 · openalex updated_date 2026/08/05
We compute the rational \mathfraksl2 R-matrix acting in the product of two spin-ℓ\over 2 (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.