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Codimensions of Newton strata for SL 3(F) in the Iwahori case

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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Beazley, E.T. Codimensions of Newton strata for SL 3(F) in the Iwahori case. Math. Z. 263, 499–540 (2009). https://doi.org/10.1007/s00209-008-0429-z

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  • DOI: https://doi.org/10.1007/s00209-008-0429-z

Keywords

  • Newton polygon
  • Newton stratification
  • Isocrystal
  • Affine Bruhat decomposition
  • Affine Deligne–Lusztig variety
  • Frobenius-linear characteristic polynomial

Mathematics Subject Classification (2000)

  • Primary 20G25
  • Secondary 14L05