Quantum super-spherical pairs

TL;DR

This paper introduces quantum super-spherical pairs, a new class of coideal subalgebras in quantum supergroups, which generalize existing quantum symmetric pairs and relate to solutions of graded reflection equations.

Contribution

It defines quantum super-spherical pairs within quantum supergroups, extending the concept of quantum symmetric pairs to a superalgebra setting.

Findings

Defines quantum super-spherical pairs as coideal subalgebras.

Shows their role as isotropy subgroups for graded reflection equations.

Generalizes previous quantum symmetric pair constructions.

Abstract

We introduce quantum super-spherical pairs as coideal subalgebras in general linear and orthosymplectic quantum supergroups. These subalgebras play a role of isotropy subgroups for matrices solving $\mathbb{Z}_2$-graded reflection equation. They generalize quantum (pseudo)-symmetric pairs of Letzter-Kolb-Regelskis-Vlaar.