Quantum supersymmetric pairs of basic types

Abstract

We formulate and classify super Satake diagrams under a mild assumption, building on arbitrary Dynkin diagrams for finite-dimensional basic Lie superalgebras. We develop a theory of quantum supersymmetric pairs associated to the super Satake diagrams. We establish the quantum Iwasawa decomposition and construct quasi $K$-matrix associated with the quantum supersymmetric pairs. We also formulate a Schur duality between an $\imath$quantum supergroup (which is a new $q$-deformation of an ortho-symplectic Lie superalgebra) and the $q$-Brauer algebra.