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arXiv · 2306.05933

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

Felix Schremmer
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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-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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Felix Schremmer. 2023-06-09. Affine Deligne-Lusztig varieties via the double Bruhat graph I: Semi-infinite orbits. https://doi.org/10.2140/ant.2025.19.1973

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