Introduction to Hecke Algebras

In this series we will focus on one particular algebra, namely the Hecke algebra. In the first talk we will discuss how this algebra arises as a certain convolution algebra and discuss its basic structural properties. If time permits, we may introduce a special kind of representation called a W-graph representation. The second talk will be devoted to the well known paper of Gyoja, which proves that (in case of finite Weyl groups), any irreducible representation carries a W-graph basis.