Braid Group Action and Quantum Queer Superalgebra

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.