Irreducible components of minuscule affine Deligne-Lusztig varieties

Abstract

We examine the set of $J_b(F)$-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.

21 pages, v2: small corrections, removed Lemma 1.3

References in corpus (3)

• The geometry of Newton strata in the reduction modulo $p$ of Shimura varieties of PEL type
• The almost product structure of Newton strata in the Deformation space of a Barsotti-Tate group with crystalline Tate tensors
• The dimension of affine Deligne-Lusztig varieties in the affine Grassmannian of unramified groups

Cited by in corpus (4)

• Central elements in affine mod $p$ Hecke algebras via perverse ${\mathbb{F}}_p$-sheaves
• Equidimensionality of affine Deligne-Lusztig varieties in mixed characteristic
• Affine Deligne-Lusztig varieties via the double Bruhat graph II: Iwahori-Hecke algebra
• Mod $p$ points on Shimura varieties of parahoric level (with an appendix by Rong Zhou)