Basic Loci of Positive Coxeter Type for $G{L}_n$

Motivated by the problem of giving an explicit description of the basic locus in the reduction of Shimura varieties, Görtz, He and Nie studied the cases where the basic affine Deligne-Lusztig variety, which serves as its group-theoretic model, is a union of classical Deligne-Lusztig varieties associated to Coxeter elements. In this paper, we study a natural generalization of this stratification in the case of $G{L}_n$.