Representations of $gl(m|n)$ in char. 0 and in char $p>2$

A Lie superalgebra is a generalization of Lie algebra to include a $Z_2$ grading. Definitions of, such as, a Lie superalgebra, homomorphism, and module, etc., resemble the Lie algebra case but include a suitable sign twist everywhere. The complexity of representation theory of Lie superalgebras far exceeds that of Lie algebras. For example, the finite-dimensional representations /C is not complete reducible for most complex simple Lie superalgbras. In this talk, I will be focusing on the general linear Lie superalgebra $gl(m|n)$, I will try to sketch rough pictures of the representation theory of $gl(m|n)$ both over the complex numbers and over char. $p>2$. The only prerequisite is some acquaintance of Lie algebras.