Vol. 12, No. 7, 2018

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Irreducible components of minuscule affine Deligne–Lusztig varieties

Paul Hamacher and Eva Viehmann

Vol. 12 (2018), No. 7, 1611–1634
Abstract

We examine the set of Jb(F)-orbits in the set of irreducible components of affine Deligne–Lusztig varieties for a hyperspecial subgroup and minuscule coweight μ. Our description implies in particular that its number of elements is bounded by the dimension of a suitable weight space in the Weyl module associated with μ of the dual group.

Keywords
affine Deligne–Lusztig variety, Rapoport–Zink spaces, affine Grassmannian
Mathematical Subject Classification 2010
Primary: 14G35
Secondary: 20G25
Milestones
Received: 7 March 2017
Revised: 28 December 2017
Accepted: 30 March 2018
Published: 27 October 2018
Authors
Paul Hamacher
Fakultät für Mathematik
Technische Universität München
Garching bei München
Germany
Eva Viehmann
Fakultät für Mathematik
Technische Universität München
Garching bei München
Germany