Crystal bases for the quantum queer superalgebra

Details Crystal bases for the quantum queer superalgebra Crystal bases for the quantum queer superalgebra

2011-03-17

arxiv.org/abs/1103.3437v2

Mathematics

Representation Theory

38 pages

Scientific paper

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
$O_int^{\geq 0}$. Our main theorem shows that every $U_q(\mathfrak
q(n))$-module in the category $O_int^{\geq 0}$ has a unique crystal basis.

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