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In [Wyser-Yong '13] we introduced polynomial representatives of cohomologyclasses of orbit closures in the flag variety, for the symmetric pair$(GL_{p+q}, GL_p \times GL_q)$. We present analogous results for the remainingsymmetric pairs of the form $(GL_n,K)$, i.e., $(GL_n,O_n)$ and$(GL_{2n},Sp_{2n})$. We establish the well-definedness of certainrepresentatives from [Wyser '13]. It is also shown that the representativeshave the combinatorial properties of nonnegativity and stability. Moreover, wegive some extensions to equivariant $K$-theory.

Polynomials for symmetric orbit closures in the flag variety