# Affine Deligne-Lusztig varieties associated with generic Newton points

@inproceedings{He2021AffineDV, title={Affine Deligne-Lusztig varieties associated with generic Newton points}, author={Xuhua He}, year={2021} }

This paper gives an explicit formula of the dimension of affine Deligne-Lusztig varieties associated with generic Newton point in terms of Demazure product of Iwahori-Weyl groups. To George Lusztig with admiration

#### References

SHOWING 1-10 OF 16 REFERENCES

Hecke algebras and $p$-adic groups

- Mathematics
- 2015

This survey article, is written as an extended note and supplement of my lectures in the current developments in mathematics conference in 2015. We discuss some recent developments on the conjugacy… Expand

A geometric interpretation of Newton strata

- Mathematics
- 2018

The Newton strata of a reductive $p$-adic group are introduced in \cite{Newton} and play some role in the representation theory of $p$-adic groups. In this paper, we give a geometric interpretation… Expand

Centers and cocenters of 0-Hecke algebras

- Mathematics
- 2015

In this paper, we give explicit descriptions of the centers and cocenters of 0-Hecke algebras associated to finite Coxeter groups.

Affine Grassmannians and the geometric Satake in mixed characteristic

- Mathematics
- 2014

We endow the set of lattices in Q_p^n with a reasonable algebro-geometric structure. As a result, we prove the representability of affine Grassmannians and establish the geometric Satake… Expand

GEOMETRIC AND HOMOLOGICAL PROPERTIES OF AFFINE DELIGNE-LUSZTIG VARIETIES

- Mathematics
- 2012

This paper studies ane Deligne-Lusztig varieties X ~ w(b) in the ane ag variety of a quasi-split tamely ramied group. We describe the geometric structure of X ~ w(b) for a minimal length element ~ w… Expand

Generic Newton points and the Newton poset in Iwahori-double cosets

- Mathematics
- Forum of Mathematics, Sigma
- 2020

Abstract We consider the Newton stratification on Iwahori-double cosets in the loop group of a reductive group. We describe a group-theoretic condition on the generic Newton point, called cordiality,… Expand

A guide to the reduction modulo p of Shimura varieties

- Mathematics
- 2002

This is a report on results and methods in the reduction modulo p of Shimura varieties with parahoric level structure. In the first part, the local theory, we explain the concepts of parahoric… Expand

Kottwitz-Rapoport conjecture on unions of affine Deligne-Lusztig varieties

- Mathematics
- 2014

In this paper, we prove a conjecture of Kottwitz and Rapoport on a union of (generalized) affine Deligne-Lusztig varieties $X(\mu, b)_J$ for any tamely ramified group $G$ and its parahoric subgroup… Expand

Maximal Newton Points and the Quantum Bruhat Graph

- Mathematics
- 2016

We discuss a surprising relationship between the partially ordered set of Newton points associated to an affine Schubert cell and the quantum cohomology of the complex flag variety. The main theorem… Expand

Truncations of level 1 of elements in the loop group of a reductive group

- Mathematics
- 2009

The aim of this article is to dene and study a new invariant of elements of loop groups that is invariant under -conjugation by a hyperspecial maximal open subgroup and that we call the truncation of… Expand