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## 0-cycles on Grassmannians as representations of projective groups

Given two fields k and F, a k-vector space V, an integer r≥1, we study the structure of the F-representation of the projective group PGL(V) in the F-vector space of formal finite linear combinations with coefficients in F of r-dimensional vector subspaces of V.  This gives a series of natural examples of irreducible infinite-dimensional representations of projective groups. These representations are non-smooth when k is a local field.