Quantum supergroups V. Braid group action

TL;DR

This paper constructs a braid group action on quantum covering groups and uses it to develop a PBW basis with orthogonality properties, advancing the algebraic understanding of quantum supergroups.

Contribution

It introduces a new braid group action on quantum covering groups and constructs a PBW basis with orthogonality, based on operators satisfying spin braid relations.

Findings

Braid group action on quantum covering groups is established.

A PBW basis for the positive half is constructed with orthogonality.

Operators satisfy spin braid relations, enabling the basis construction.

Abstract

We construct a braid group action on quantum covering groups. We further use this action to construct a PBW basis for the positive half in finite type which is pairwise-orthogonal under the inner product. This braid group action is induced by operators on the integrable modules; however, these operators satisfy spin braid relations.