Affine Deligne–Lusztig varieties and quantum Bruhat graph

In this paper, we consider affine Deligne–Lusztig varieties X w ( b ) and their certain union X ( μ , b ) inside the affine flag variety of a reductive group. Several important results in the study of affine Deligne–Lusztig varieties have been established under the so-called superregularity hypothes...

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Bibliographic Details
Published in:Mathematische Zeitschrift Vol. 303; no. 1; p. 21
Main Author: Sadhukhan, Arghya
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2023
Springer Nature B.V
Subjects:
Hypotheses
Mathematics
Mathematics and Statistics
11G25
Affine Deligne–Lusztig variety
Dimension formula
20G25
Affine Weyl group
Generic Newton point
20F55
ISSN:0025-5874, 1432-1823
Online Access:Get full text
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Summary:In this paper, we consider affine Deligne–Lusztig varieties X w ( b ) and their certain union X ( μ , b ) inside the affine flag variety of a reductive group. Several important results in the study of affine Deligne–Lusztig varieties have been established under the so-called superregularity hypothesis. Such results include a description of generic Newton points in Iwahori double cosets of loop groups, covering relation in the associated Iwahori–Weyl group and a dimension formula for X ( μ , b ) . We show that one can considerably weaken the superregularity hypothesis and sometimes eliminate it, thus strengthening these existing results.
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ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-022-03154-w