Braid Group Action and Quantum Queer Superalgebra

TL;DR

This paper constructs explicit braid group actions on quantum queer superalgebras, introduces new root vector definitions, and derives a PBW-type basis, advancing the algebraic understanding of these structures.

Contribution

It provides explicit braid group actions and a new root vector framework for quantum queer superalgebras, along with a PBW basis construction.

Findings

Explicit braid group actions on superalgebras

New definitions of root vectors

PBW-type basis for quantum queer superalgebras

Abstract

In this paper, we present explicit actions of braid group on the universal enveloping superalgebra ${\boldsymbol U}(\mathfrak{{q}}_n)$ and the quantum queer superalgebra ${\boldsymbol U}_{\!{v}}(\mathfrak{{q}}_{n})$. Then we provide a new definition of root vectors and some explicit expression for them. With these procedures, we obtain the PBW-type basis containing the product of root vectors.