Geometric Structure of Affine Deligne-Lusztig Varieties for $GL_3$

DOI10.1016/J.JALGEBRA.2023.02.015zbMATH Open1517.14035arXiv2102.09169MaRDI QIDQ6360929

Publication date: 18 February 2021

Abstract: In this paper we study the geometric structure of affine Deligne-Lusztig varieties for

G L_{3}

and

b

basic. We completely determine the irreducible components of the affine Deligne-Lusztig variety. In particular, we classify the cases where all of the irreducible components are classical Deligne-Lusztig varieties times finite-dimensional affine spaces. If this is the case, then the irreducible components are pairwise disjoint.

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Grassmannians, Schubert varieties, flag manifolds (14M15)

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