Involution pipe dreams

Abstract Involution Schubert polynomials represent cohomology classes of K -orbit closures in the complete flag variety, where is orthogonal or symplectic group. We show they also $\mathsf {T}$ -equivariant subvarieties defined by upper-left rank conditions spaces symmetric skew-symmetric matrices. This geometry implies that these are positive combinations monomials variables $x_i + x_j$ , and we give explicit formulas this kind as sums over new objects called involution pipe dreams. Our analogues Billey–Jockusch–Stanley formula for polynomials. In Knutson Miller’s approach to matrix varieties, dream reflect Gröbner degenerations ideals those conjecturally identify analogous our setting.