The dual flagged Weyl character is zero-one if and only if the defining diagram is multiplicity-free, namely it avoids twelve listed subconfigurations up to column swap.
Brion, Multiplicity-free subvarieties of flag varieties, Commuta tive algebra (Grenoble/Lyon, 2001), Contemp
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Zero-one dual characters of flagged Weyl modules
The dual flagged Weyl character is zero-one if and only if the defining diagram is multiplicity-free, namely it avoids twelve listed subconfigurations up to column swap.