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Grassmannians are algebraic varieties whose points corresponds to vector subspaces of a fixed dimension in a fixed vector space.
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How to obtain an quantization of the algebra of functions of a given space?
Therefore to be more explicit: Given a (complex) Grassmannian $Gr(n,m)$, how to define the algebra of functions on the total space of a family of quantum Grassmannians? … use the definition o f S.Launois and T.H.Lenagan given in "Twisting the quantum grassmannian" to define such algebras, but from that we will obtain (I suspect so) the, what we call, standard quantum Grassmannians …