Closure of Steinberg fibers and affine Deligne-Lusztig varieties
Abstract
We discuss some connections between the closure F of a Steinberg fiber in the wonderful compactification of an adjoint group and the affine Deligne-Lusztig varieties Xw(1) in the affine flag variety. Among other things, we describe the emptiness/nonemptiness pattern of Xw(1) if the translation part of w is quasi-regular. As a by-product, we give a new proof of the explicit description of F, first obtained in H1.
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