Title: |
Lattice paths for characters, the Virasoro algebra and the superconformal algebra Computing with real Lie algebras |

Speaker: |
Trevor Welsh (University of Melbourne) |

Abstract: |
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 sl 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. |