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Super Grassmannians are introduced by Manin, see for example. We have Plucker relation for Grassmannian.

Are there some references about super Plucker relations for super Grassmannian? Thank you very much.

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In The quantum chiral Minkowski and conformal superspaces by Cervantes, Fioresi, and Lledó the super Grassmannian of $(2|0)$ planes in $\mathbb{C}^{4|1}$ is considered. In Equation (4.9) some "super Plücker relations" are given for this particular super Grassmannian. The relations contain the classical Plücker relation for $Gr(2,4)$ plus some more relations.

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There's a paper titled On super Plücker embedding and possible application to cluster algebras just came out this summer.

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