Affine Deligne-Lusztig varieties in affine flag varieties
Ulrich Goertz, Thomas J. Haines, Robert E. Kottwitz, Daniel C. Reuman
TL;DR
This paper investigates affine Deligne-Lusztig varieties within affine flag varieties, establishing conditions for their emptiness, relating them to Levi subgroups, and extending conjectures on their dimensions and methods.
Contribution
It introduces new results on the structure, emptiness, and dimensions of affine Deligne-Lusztig varieties, generalizing previous conjectures and methods.
Findings
Proves emptiness for certain affine Deligne-Lusztig varieties
Relates varieties to those for Levi subgroups
Extends conjectures on their dimensions and generalizes the superset method
Abstract
This paper studies affine Deligne-Lusztig varieties in the affine flag manifold of a split group. Among other things, it proves emptiness for certain of these varieties, relates some of them to those for Levi subgroups, extends previous conjectures concerning their dimensions, and generalizes the superset method.
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