On the Topology of the Combinatorial Flag Varieties

We prove that the simplicial complex Ωn of chains of matroids (with respect to the ordering by the quotient relation) on n elements is shellable. This follows from a more general result on shellability of the simplicial complex of W -matroids for an arbitrary finite Coxeter group W , and generalises the well-known results by Solomon—Tits and Björner on spherical buildings.

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