# Martina Lanini (University of Melbourne)

## Friday 30th August, 12:05-12:55pm, Carslaw 373

### Towards a moment graph approach to critical level representation theory

Moment graph techniques have been applied in the study of non-critical blocks of category $$O$$ for affine Kac-Moody algebras, while in the critical case these methods have not been developed yet. Inspired by the fact that non-critical representations are controlled by the Hecke algebra $$H$$, while critical level representations are expected to be governed by the periodic module $$M$$, we prove the moment graph analogue of a result by Lusztig which bridges $$H$$ and $$M$$, and believe that it should provide us with new tools to attack the critical level case.