Graded Satake diagrams and super-symmetric pairs

TL;DR

This paper classifies classical spherical subalgebras in basic matrix Lie superalgebras and their Satake diagrams, establishing their quantization to coideal subalgebras in quantum supergroups.

Contribution

It provides a comprehensive classification of Satake-type diagrams and demonstrates their role in defining families of proper spherical subalgebras.

Findings

List of classical spherical subalgebras in basic matrix Lie superalgebras.

Classification of Satake-type diagrams for these subalgebras.

Proof that each diagram defines a family of proper spherical subalgebras.

Abstract

We list classical spherical subalgebras in basic matrix Lie superalgebras which are quantizable to coideal subalgebras in the standard quantum supergroups, for any choice of Borel subalgebra. We classify the corresponding Satake-type diagrams and prove that each of them defines a family of proper spherical subalgebras.