Affine Deligne–Lusztig varieties via the double Bruhat graph, I : Semi-infinite orbits

IF 1 1区数学 Q2 MATHEMATICS

Algebra & Number Theory Pub Date : 2025-09-05 DOI:10.2140/ant.2025.19.1973

Felix Schremmer

引用次数: 0

Abstract

We introduce a new language to describe the geometry of affine Deligne–Lusztig varieties in affine flag varieties. This first part of a two-paper series develops the definition and fundamental properties of the double Bruhat graph by studying semi-infinite orbits. This double Bruhat graph was originally introduced by Naito and Watanabe to study periodic $R$ -polynomials. We use it to describe the geometry of many affine Deligne–Lusztig varieties, overcoming a previously ubiquitous regularity condition.

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通过重Bruhat图的仿射delig - lusztig变分，I：半无限轨道

我们引入了一种新的语言来描述仿射标志变体中的仿射delign - lusztig变体的几何形状。这是两篇论文系列的第一部分，通过研究半无限轨道，发展了重Bruhat图的定义和基本性质。这个双Bruhat图最初是由内藤和渡边引入来研究周期r多项式的。我们用它来描述许多仿射delign - lusztig变体的几何，克服了以前普遍存在的正则条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algebra & Number Theory MATHEMATICS-

CiteScore

1.80

自引率

7.70%

发文量

审稿时长

6-12 weeks

期刊介绍： ANT’s inclusive definition of algebra and number theory allows it to print research covering a wide range of subtopics, including algebraic and arithmetic geometry. ANT publishes high-quality articles of interest to a broad readership, at a level surpassing all but the top four or five mathematics journals. It exists in both print and electronic forms. The policies of ANT are set by the editorial board — a group of working mathematicians — rather than by a profit-oriented company, so they will remain friendly to mathematicians'' interests. In particular, they will promote broad dissemination, easy electronic access, and permissive use of content to the greatest extent compatible with survival of the journal. All electronic content becomes free and open access 5 years after publication.