Abstract: In Part I, we explain in detail the major differences between representation theory of Lie superalgebras and its Lie algebra counterpart. We show how the Schur-Jimbo duality allows for a reformulation of Kazhdan-Lusztig theory for type A, which further affords for a generalization to general linear Lie superalgebras (known as Brundan's KL conjecture, now a theorem); this is joint work with Shun-Jen Cheng and Ngau Lam.

Abstract of Part II