Quantum supersymmetric pairs of basic types
arXiv:2408.02874 · doi:10.1007/s00220-025-05339-w
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 -matrix associated with the quantum supersymmetric pairs. We also formulate a Schur duality between an quantum supergroup (which is a new -deformation of an ortho-symplectic Lie superalgebra) and the -Brauer algebra.
44 pages, 4 tables, many diagrams; v2, 47 pages, major revision, corrected mistakes including Table 3, reference updated