Irreducible components of minuscule affine Deligne–Lusztig varieties

Abstract

We examine the set of $J_b\left(F\right)$-orbits in the set of irreducible components of affine Deligne–Lusztig varieties for a hyperspecial subgroup and minuscule coweight $\mu$. Our description implies in particular that its number of elements is bounded by the dimension of a suitable weight space in the Weyl module associated with $\mu$ of the dual group.