Seminars

3pm Thursday 6 November 2008, Lecture theatre S14
School of Mathematical Sciences Colloquium
Beads on runners
Arun Ram, Melbourne University

We think of beads on runners like an abacus, or like one of those games for toddlers where the children slide the beads on the runners (these games are sometimes found in waiting rooms of the offices of pediatricians). In joint work with A. Kleshchev we have shown this is a perfect model for representations of Khovanov-Lauda algebras, the recently discovered algebras whose representations categorify quantum groups. I shall explain the bead and runner model and how to have your toddlers compute representations of Khovanov-Lauda algebras while waiting for the doctor at the medical centre. The model generalizes partitions and their classical connection to the symmetric group. At the end of the talk I will explain how these algebras are related to Lie algebras and quantum groups and why they are considered a great new advance in the art of "categorification".