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Affine Deligne–Lusztig varieties in affine flag varieties

Published online by Cambridge University Press:  07 July 2010

Ulrich Görtz
Affiliation:
Institut für Experimentelle Mathematik, Universität Duisburg-Essen, Ellernstrasse 29, 45326 Essen, Germany (email: ulrich.goertz@uni-due.de)
Thomas J. Haines
Affiliation:
Department of Mathematics, University of Maryland, College Park, Maryland 20742-4015, USA (email: tjh@math.umd.edu)
Robert E. Kottwitz
Affiliation:
Department of Mathematics, University of Chicago, 5734 South University Avenue, Chicago, Illinois 60637, USA (email: kottwitz@math.uchicago.edu)
Daniel C. Reuman
Affiliation:
Imperial College London, Silwood Park Campus, Buckhurst Road, Ascot, Berkshire SL5 7PY, UK (email: d.reuman@imperial.ac.uk)
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Abstract

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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, and extends previous conjectures concerning their dimensions. We generalize the superset method, an algorithmic approach to the questions of non-emptiness and dimension. Our non-emptiness results apply equally well to the p-adic context and therefore relate to moduli of p-divisible groups and Shimura varieties with Iwahori level structure.

Type
Research Article
Copyright
Copyright © Foundation Compositio Mathematica 2010

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