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The subgroup K=GL_p x GL_q of GL_{p+q} acts on the (complex) flag varietyGL_{p+q}/B with finitely many orbits. We introduce a family of polynomials thatspecializes to representatives for cohomology classes of the orbit closures inthe Borel model. We define and study K-orbit determinantal ideals to supportthe geometric naturality of these representatives. Using a modification ofthese ideals, we describe an analogy between two local singularity measures:the H-polynomials and the Kazhdan-Lusztig-Vogan polynomials.

Polynomials for GL_p x GL_q orbit closures in the flag variety