Title: Lattice paths for characters, the Virasoro algebra and the superconformal algebra Computing with real Lie algebras
Speaker: Trevor Welsh (University of Melbourne)

The connection between the Dyck-type lattice paths and mathematical physics came to prominence in the work of Andrews, Baxter and Forrester on the eight-vertex RSOS statistical models. The connection with the representation theory of affine sl2 and minimal models of the Virasoro algebra spurred the development of quantum groups, for which the lattice paths arise naturally in crystal graphs.

After briefly reviewing the above, we develop similar connections between the Motzkin and Riordan-type lattice paths and the representation theory of the other affine Lie algebras and minimal models. The Motzkin and Riordan-type paths are combined under the umbrella notion of "half-lattice" paths. These paths are then amenable to combinatorial methods, previously developed by Foda and the speaker for the Dyck-type paths, that lead to fermionic-type expressions for the various characters.