# Minimal Newton strata in Iwahori double cosets

## TL;DR

This paper investigates the structure of Newton strata within Iwahori double cosets in loop groups, identifying minimal elements and computing their dimensions under certain conditions, with implications for affine Deligne-Lusztig varieties.

## Contribution

It establishes the existence and uniqueness of minimal Newton strata in Iwahori double cosets for unramified groups and computes their dimensions under regularity assumptions.

## Key findings

- Unique minimal Newton element identified in Iwahori double cosets
- Dimension formulas for Newton strata under regularity conditions
- Results extended to affine Deligne-Lusztig varieties

## Abstract

The set of Newton strata in a given Iwahori double coset in the loop group of a reductive group G is indexed by a finite subset of the set B(G) of Frobenius-conjugacy classes. For unramified $G$ we show that it has a unique minimal element and determine this element. Under a regularity assumption we also compute the dimension of the corresponding Newton stratum. We derive corresponding results for affine Deligne-Lusztig varieties.