Quantum supersymmetric pairs of basic types

TL;DR

This paper develops a classification of super Satake diagrams, constructs quantum supersymmetric pairs, and establishes dualities and decompositions in the context of quantum supergroups related to Lie superalgebras.

Contribution

It introduces a new classification framework for super Satake diagrams and develops the theory of quantum supersymmetric pairs with associated dualities.

Findings

Classification of super Satake diagrams under mild assumptions

Construction of quantum supersymmetric pairs and quasi K-matrix

Establishment of Schur duality between quantum supergroup and q-Brauer algebra

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.