Quantum Queer Superalgebra and Crystal Bases

In this paper, we develop the crystal basis theory for the quantum queer superalgebra $\text{Uq}$. We define the notion of crystal bases, describe the tensor product rule, and present the existence and uniqueness of crystal bases for finite-dimensional $\text{Uq}$-modules in the category ${\mathcal{O}}_{int}^{\ge 0}$.