TL;DR
This paper explores affine Lusztig varieties, revealing their connection to affine Deligne--Lusztig varieties, and provides explicit criteria for their nonemptiness and dimension in most cases.
Contribution
It establishes a precise relationship between affine Lusztig and affine Deligne--Lusztig varieties, offering explicit nonemptiness and dimension formulas.
Findings
Explicit nonemptiness pattern for affine Lusztig varieties
Dimension formulas for most cases of affine Lusztig varieties
Connection established between affine Lusztig and affine Deligne--Lusztig varieties
Abstract
Affine Lusztig varieties encode the orbital integrals of Iwahori--Hecke functions and serve as building blocks for the (conjectural) theory of affine character sheaves. We establish a close relationship between affine Lusztig varieties and affine Deligne--Lusztig varieties. Consequently, we give an explicit nonemptiness pattern and dimension formula for affine Lusztig varieties in most cases.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Mathematical Identities · Algebraic structures and combinatorial models