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

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.

arXiv comment44 pages; many details clarified and corrected; comments appreciated

References in corpus (6)

• A uniform model for Kirillov-Reshetikhin crystals I: Lifting the parabolic quantum Bruhat graph
• Affine Deligne-Lusztig varieties in affine flag varieties
• Twisted orbital integrals and irreducible components of affine Deligne-Lusztig varieties
• The geometry of Newton strata in the reduction modulo $p$ of Shimura varieties of PEL type
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Cited by in corpus (1)

• Affine Deligne-Lusztig varieties via the double Bruhat graph II: Iwahori-Hecke algebra