Mathematical Sciences Department Colloquium
Speaker: Paul Terwilliger, University of Wisconsin
Friday, January 17th
11:00 - 11:50 am
Stratton Hall 202
Title: The subconstituent algebra of a graph, the $Q$-polynomial property, and tridiagonal pairs of linear transformations
Abstract: This survey talk has two parts. In Part I, we review the subconstituent algebra $T$ of a graph. We will discuss the $Q$-polynomial assumption, under which $T$ is well behaved. Motivated by the first part, in Part II we discuss a linear-algebraic object called a tridiagonal pair. A tridiagonal pair consists of two diagonalizable linear transformations on a nonzero finite dimensional vector space, that each act in a (block)-tridiagonal fashion on the eigenspaces of the other one. We will discuss the classification of tridiagonal pairs, and describe in detail a special case called a Leonard pair. This talk is meant for a general mathematical audience.