Polynomials for symmetric orbit closures in the flag variety

Abstract

In [Wyser-Yong '13] we introduced polynomial representatives of cohomology classes of orbit closures in the flag variety, for the symmetric pair $(G{L}_{p+q},G{L}_p\times G{L}_q)$. We present analogous results for the remaining symmetric pairs of the form $(G{L}_n,K)$, i.e., $(G{L}_n,O_n)$ and $(G{L}_{2n},S{p}_{2n})$. We establish the well-definedness of certain representatives from [Wyser '13]. It is also shown that the representatives have the combinatorial properties of nonnegativity and stability. Moreover, we give some extensions to equivariant $K$-theory.

22 pages, 3 figures, 5 tables. Results from V1 have been extended significantly

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