Semi-modules and crystal bases via affine Deligne-Lusztig varieties

Abstract

There are two combinatorial ways of parameterizing the Jb(F)-orbits of the irreducible components of affine Deligne-Lusztig varieties for GLn and superbasic b. One way is to use the extended semi-modules introduced by Viehmann. The other way is to use the crystal bases introduced by Kashiwara and Lusztig. In this paper, we give an explicit correspondence between them using the crystal structure.