RTGC and $K$-theory seminar: Character Formulas for Matrix Factorisations

Seminar | May 2 | 11:10 a.m.-12:30 p.m. | 732 Evans Hall

 Kiran Luecke, Oxford University and UC Berkeley

 Department of Mathematics

Using the structure of the matrix factorisation category $\mathrm{MF}_G(\mathfrak g, W)$ of Freed and Teleman, I deduce the Kirillov character formula for compact Lie groups, and the Rossman character formula for the discrete series of a real semi-simple Lie group. The proofs are a calculation of Chern characters and use the Dirac family constructed by Freed, Hopkins, and Teleman. Indeed, one of the main results of their work is a categorification of the Kirillov correspondence, and in this talk I’ll give show that this correspondence can be recovered at the level of characters.