Symmetric Dellac configurations and symplectic/orthogonal flag varieties

The goal of this paper is to study the link between the topology of the degenerate flag varieties and combinatorics of the Dellac configurations. We define three new classes of algebraic varieties closely related to the degenerate flag varieties of types A and C. The definitions are given in terms of linear algebra: they are based on the quiver Grassmannian realization of the degenerate flag varieties and odd symplectic and odd and even orthogonal groups. We study basic properties of our varieties; in particular, we construct cellular decomposition in all the three cases above (as well as in the case of even symplectic group). We also compute the Poincaré polynomials in terms of certain statistics on the set of symmetric Dellac configurations.