Totally nonnegative Grassmannians were introduced and studied by Postnikov. In short,
these are subsets of the real Grassmann varieties
consisting of points whose Pluecker coordinates have the same sign. The tnn
Grassmannians enjoy a lot of nice algebraic, topological
and combinatorial properties. In particular, they admit cellular decompositions with
explicitly described posets of cells. We construct
complex algebraic varieties admitting a decomposition into complex cells with the
corresponding poset being dual to that of the
tnn Grassmannians. Our varieties are realized as quiver Grassmannians for the cyclic
quivers. The quiver Grassmannians we consider
also show up as local models of Shimura varieties. Joint work with Martina Lanini and
Alexander Puetz.
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