Connected components of closed affine Deligne-Lusztig varieties in affine Grassmannians
Sian Nie
TL;DR
This paper identifies the connected components of certain geometric objects called affine Deligne-Lusztig varieties within affine Grassmannians, extending previous results to more general group settings.
Contribution
It generalizes prior work by determining connected components for unramified groups, broadening the understanding of affine Deligne-Lusztig varieties.
Findings
Connected components explicitly characterized for unramified groups.
Extension of previous split reductive group results.
Broader applicability to affine Grassmannian geometry.
Abstract
We determine the set of connected components of closed affine Deligne-Lusztig varieties for hyperspecial maximal parahoric subgroups of unramified connected reductive groups. This extends the work by Viehmann for split reductive groups, and the work by Chen-Kisin-Viehmann on minuscule affine Deligne-Lusztig varieties.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Algebraic structures and combinatorial models