Abstract:

Affine Deligne-Lusztig varieties are closely related to basic loci in Shimura varieties. The conjecture by Miaofen Chen and Xinwen Zhu states that irreducible components of affine Deligne-Lusztig varieties are parametrized by a weight space of the crystal basis (or the canonical basis) constructed by Kashiwara and Lusztig. While this conjecture has recently been proved, stronger results are known in some special cases. In this talk, I will propose a new conjecture generalizing the Chen-Zhu conjecture.

 

Organizer: Joseph Muller (NCTS)