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

Arnold Mathematical Journal. 2019. Vol. 5. No. 2-3. P. 373-385.
Bezrukavnikov R., Rovinsky M.

Let $F$ be an infinite division ring, $V$ be a left $F$-vector space, $r>0$ be an integer.
We study the structure of the representation of the linear group $\mathrm{GL}_F(V)$ in the vector space of formal finite linear combinations of $r$-dimensional vector subspaces of $V$ with coefficients in a field.

This gives a series of natural examples of irreducible infinite-dimensional representations of projective
groups. These representations are non-smooth if $F$ is locally compact and non-discrete.