The extended weak order for the affine and infinite symmetric groups is a profinite completely semidistributive lattice, with canonical join representations described by cyclic arc diagrams.
Barkley and David E Speyer
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Extended weak order for the affine symmetric group
The extended weak order for the affine and infinite symmetric groups is a profinite completely semidistributive lattice, with canonical join representations described by cyclic arc diagrams.