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Generic Newton points and the Newton poset in Iwahori-double cosets

Part of: Algebraic groups Special aspects of infinite or finite groups Arithmetic algebraic geometry

Published online by Cambridge University Press:  13 November 2020

Elizabeth Milićević  and
Eva Viehmann
Elizabeth Milićević
Affiliation:
Haverford College, Department of Mathematics & Statistics, 370 Lancaster Avenue, Haverford, PA, 19041, USA; E-mail: emilicevic@haverford.edu
Eva Viehmann
Affiliation:
Technische Universität München, Fakultät für Mathematik - M11, Boltzmannstr. 3, 85748 Garching bei München, Germany; E-mail: viehmann@ma.tum.de

Abstract

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We consider the Newton stratification on Iwahori-double cosets in the loop group of a reductive group. We describe a group-theoretic condition on the generic Newton point, called cordiality, under which the Newton poset (that is, the index set for non-empty Newton strata) is saturated and Grothendieck’s conjecture on closures of the Newton strata holds. Finally, we give several large classes of Iwahori-double cosets for which this condition is satisfied by studying certain paths in the associated quantum Bruhat graph.

Keywords

affine Deligne-Lusztig varietyNewton strataaffine flag variety

MSC classification

Primary: 11G25: Varieties over finite and local fields
Secondary: 14L05: Formal groups, $p$-divisible groups 20F55: Reflection and Coxeter groups
Type
Number Theory
Information
Forum of Mathematics, Sigma , Volume 8 , 2020 , e50
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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