The strong Macdonald conjecture and Hodge theory on the Loop Grassmannian

Susanna Fishel, Ian Grojnowski, Constantin Teleman

We prove the strong Macdonald conjecture of Hanlon and Feigin for reductive groups G. In a geometric reformulation, we show that the Dolbeault cohomology $H^q(X;{\Omega }^p)$ of the loop G…