Hybrid generic pipe dreams give a hybridization-independent equivariant formula for the classes of lower-upper varieties, proved via Yang-Baxter equations and a degeneration into complete intersections.
Back stable Schubert calculus
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We study the back stable Schubert calculus of the infinite flag variety. Our main results are: 1) a formula for back stable (double) Schubert classes expressing them in terms of a symmetric function part and a finite part; 2) a novel definition of double and triple Stanley symmetric functions; 3) a proof of the positivity of double Edelman-Greene coefficients generalizing the results of Edelman-Greene and Lascoux-Schutzenberger; 4) the definition of a new class of bumpless pipedreams, giving new formulae for double Schubert polynomials, back stable double Schubert polynomials, and a new form of the Edelman-Greene insertion algorithm; 5) the construction of the Peterson subalgebra of the infinite nilHecke algebra, extending work of Peterson in the affine case; 6) equivariant Pieri rules for the homology of the infinite Grassmannian; 7) homology divided difference operators that create the equivariant homology Schubert classes of the infinite Grassmannian.
fields
math.CO 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Hybrid pipe dreams for the lower-upper scheme
Hybrid generic pipe dreams give a hybridization-independent equivariant formula for the classes of lower-upper varieties, proved via Yang-Baxter equations and a degeneration into complete intersections.