Crystal Bases for the Quantum Superalgebra $U_q(gl(m,n))$

Abstract

We develop a crystal base theory for the general linear Lie superalgebra $gl(m,n)$. We prove that any irreducible $U_q(gl(m,n))$-module in some category has a crystal base, and prove that its associated crystal base is parameterized by semistandard tableaux.

55 pages, many figures drawn with "texdraw"