RTGC Seminar: Character Formulas from Matrix Factorisations

Kiran Luecke, University of Oxford

Using the structure of the matrix factorisation category $MF_G(g, W)$ 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 semisimple 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 show that this correspondence can be recovered at the level of characters.