Quantum Queer Superalgebra and Crystal Bases

Abstract

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

arXiv comment11pages, 3 figures