Irreducible components of minuscule affine Deligne–Lusztig varieties

Hamacher, Paul; Viehmann, Eva

doi:10.2140/ant.2018.12.1611

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Irreducible components of minuscule affine Deligne–Lusztig varieties

Paul Hamacher and Eva Viehmann

Vol. 12 (2018), No. 7, 1611–1634

DOI: 10.2140/ant.2018.12.1611

Abstract

We examine the set of $J_{b} (F)$ -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

Vol. 12, No. 7, 2018