Crystal bases for the quantum queer superalgebra

Abstract

In this paper, we develop the crystal basis theory for the quantum queer superalgebra $U_q(\mathfrak{q}(n))$. We define the notion of crystal bases and prove the tensor product rule for $U_q(\mathfrak{q}(n))$-modules in the category $O_{i}n{t}^{\ge 0}$. Our main theorem shows that every $U_q(\mathfrak{q}(n))$-module in the category $O_{i}n{t}^{\ge 0}$ has a unique crystal basis.

38 pages, small changes on acknowledgement

Cited by in corpus (3)

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• Presenting queer Schur superalgebras