# Irreducible components of minuscule affine Deligne-Lusztig varieties

## TL;DR

This paper studies the structure of affine Deligne-Lusztig varieties, revealing bounds on the number of irreducible components related to weight spaces in Weyl modules, advancing understanding in algebraic geometry and representation theory.

## Contribution

It provides a description of the $J_b(F)$-orbits on irreducible components for hyperspecial subgroups and minuscule coweights, linking geometric components to representation-theoretic dimensions.

## Key findings

- Number of $J_b(F)$-orbits is bounded by the dimension of a weight space in a Weyl module.
- Explicit description of irreducible components for minuscule affine Deligne-Lusztig varieties.
- Connections established between geometric components and dual group representations.

## 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.