REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

ABSTRACT: Canonical bases of Lie algebras are bases of the corresponding quantum group with many remarkable properties, and in some cases, with deep connections to other areas of mathematics. With these bases in mind, it is natural to ask whether Lie superalgebras, a Z/2Z-braided generalization of Lie algebras, also have bases with similar properties. However, so far, there has been little progress towards understanding the general situation. In this talk, I will discuss some recent work constructing a canonical basis in some special cases using braid isomorphisms.