Relative braid group symmetries on quantum supersymmetric pairs of type sAIII

TL;DR

This paper introduces relative Coxeter groupoids and constructs intrinsic braid group symmetries for quantum supersymmetric pairs of type sAIII, expanding the understanding of symmetries in quantum algebra.

Contribution

It develops new intertwining properties of quasi K-matrices and establishes explicit formulas for braid symmetries in the super setting, generalizing previous non-super results.

Findings

Constructed intrinsic relative braid group symmetries for quantum supersymmetric pairs of type sAIII.

Derived explicit formulas for these symmetries.

Proved that the symmetries satisfy braid relations in the relative Coxeter groupoid.

Abstract

We introduce the relative Coxeter groupoid and construct intrinsic relative braid group symmetries for quantum supersymmetric pairs of type sAIII. These symmetries are constructed by establishing new intertwining properties of quasi $K$-matrices, which generalize the earlier non-super construction of Wang and the second author. We derive explicit formulas for these symmetries and prove that they satisfy the braid relations in the relative Coxeter groupoid.