Codimensions of Newton Strata for SL_3 in the Iwahori Case
E. T. Mili\'cevi\'c (Beazley)
TL;DR
This paper computes the codimensions of Newton strata within affine Bruhat components for SL_3 over Laurent series fields, linking these to affine Deligne-Lusztig varieties and providing criteria for their non-emptiness.
Contribution
It introduces a formula for Newton stratum codimensions in SL_3 and a method to determine non-emptiness of related affine Deligne-Lusztig varieties.
Findings
Derived explicit codimension formulas for Newton strata.
Established criteria for non-emptiness of affine Deligne-Lusztig varieties in SL_3.
Connected stratification properties to affine Bruhat decomposition.
Abstract
We study the Newton stratification on SL_3(F), where F is a Laurent power series field. We provide a formula for the codimensions of the Newton strata inside each component of the affine Bruhat decomposition on SL_3(F). These calculations are related to the study of certain affine Deligne-Lusztig varieties. In particular, we describe a method for determining which of these varieties is non-empty in the case of SL_3(F).
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Taxonomy
TopicsAdvanced Differential Geometry Research · Advanced Algebra and Geometry · Algebraic and Geometric Analysis