Resumen de Polynomials for GLp×GLq orbit closures in the flag variety

Benjamin J. Wyser, Alexander Yong

• The subgroup K=GLp×GLqK=GLp×GLq of GLp+qGLp+q acts on the (complex) flag variety GLp+q/BGLp+q/B with finitely many orbits. We introduce a family of polynomials specializing representatives for cohomology classes of the orbit closures in the Borel model. We define and study KK -orbit determinantal ideals to support the geometric naturality of these representatives. Using a modification of these ideals, we describe an analogy between two local singularity measures: the HH -polynomials and the Kazhdan–Lusztig–Vogan polynomials.