Work

Affine Deligne–Lusztig varieties with finite Coxeter parts

Year: 2024

Type: article

Abstract: We study affine Deligne-Lusztig varieties X w(b) when the finite part of the element w in the Iwahori-Weyl group is a partial σ -Coxeter element.We show that such w is a cordial element and X w(b) ̸ = ∅ if and only if b satisfies a certain Hodge-Newton indecomposability condition.Our main result is that for such w and b, X w(b) has a simple geometric structure: the σ -centralizer of b acts transitively on the set of irreducible components of X w(b) ; and each irreducible component is an iterated fibration over a classical Deligne-Lusztig variety of Coxeter type, and the iterated fibers are either ‫ށ‬ 1 or ‫އ‬ m .

Source: Algebra & Number Theory

DOI: 10.2140/ant.2024.18.1681

Authors: Xuhua He, Sian Nie, Qingchao Yu

Institutions: University of Hong Kong, Chinese Academy of Sciences, Academy of Mathematics and Systems Science, University of Chinese Academy of Sciences, Peking University

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid