A dimension formula of closed affine Deligne-Lusztig varieties of parahoric level

TL;DR

This paper derives a dimension formula for unions of affine Deligne-Lusztig varieties associated with parahoric level structures in split reductive groups, under generic conditions, advancing understanding of their geometric properties.

Contribution

It provides a new dimension formula for affine Deligne-Lusztig varieties at arbitrary parahoric levels, extending previous results to more general settings.

Findings

Dimension formula established for unions of affine Deligne-Lusztig varieties

Applicable to arbitrary parahoric level structures

Results under certain genericity hypotheses

Abstract

We establish a dimension formula for certain union $X^G(\mu,b)_J$ of affine Deligne-Lusztig varieties associated to arbitrary parahoric level structures of split reductive groups, under certain genericity hypotheses.