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Journal Article

Generic Newton points and the Newton poset in Iwahori double cosets


Milićević,  Elizabeth
Max Planck Institute for Mathematics, Max Planck Society;

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Milićević, E., & Viehmann, E. (2020). Generic Newton points and the Newton poset in Iwahori double cosets. Forum of Mathematics, Sigma, 8: e50. doi:10.1017/fms.2020.46.

Cite as: https://hdl.handle.net/21.11116/0000-0007-ADE7-2
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 (i.e. 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.