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

  • Part of
  • Elizabeth Milićević, Eva Viehmann
  • Journal:
    Forum of Mathematics, Sigma / Volume 8 / 2020
    Published online by Cambridge University Press:
    13 November 2020, e50
    • Article
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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.