Irreducibility of local models is classified by double quotients of relative Weyl groups, and all fibers of level-changing maps are single Schubert varieties.
Affin e Deligne- Lusztig varieties in affine flag varieties
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Irreducibility of Local Models
Irreducibility of local models is classified by double quotients of relative Weyl groups, and all fibers of level-changing maps are single Schubert varieties.