In this talk I will define a linear algebraic object called a bidiagonal pair. Roughly speaking, a bidiagonal pair is a pair of diagonalizable linear transformations on a finite dimensional vector space that act bidiagonally on each others eigenspaces. I will discuss how bidiagonal pairs are connected to the quantum group . In particular, I will give a presentation of by generators and relations which differs from the usual presentation. Using this new presentation I will discuss how to classify bidiagonal pairs in terms of finite dimensional represenatations of .
Bidiagonal pairs and the quantum group