University of Sydney Algebra Seminar
Jiuzu Hong
Friday 21 February, 12-1pm, in the SMRI Seminar room (McLeay Building A12, Room 301)
A comparison theorem for affine Demazure modules
Given an integrable highest weight representation \(L(\Lambda)\) of an affine Lie algebra \(\hat{g}\) associated to a simple Lie algebra \(g\), we consider a summation of certain affine Demazure modules in \(L(\Lambda)\). We show that the character of this summation with respect to the Cartan subalgebra \(h\) of \(g\), up to a shift of \(\Lambda\) restricted to \(h\), is dependent only on the level of \(L(\Lambda)\). This result refines the coherence conjecture by Pappas-Rapoport, which was proven by Zhu and focuses on comparing dimensions. To establish this comparison theorem, we investigate line bundles on global Schubert varieties of parahoric Bruhat-Tits group schemes and equip them with certain equivariant structures. This talk will be based on a joint work with Huanhuan Yu.