Quantum bumpless pipe dreams

Schubert polynomials are polynomial representatives of Schubert classes in the cohomology of the complete flag variety and have a rich combinatorial theory. In particular, their monomial expansion is given by a bumpless pipe dream formula. Quantum double Schubert polynomials are polynomial representatives of Schubert classes in the torus-equivariant quantum cohomology of the complete flag variety. In this talk, we will first review the bumpless pipe dreams formula for double Schubert polynomials. Then we will describe a generalization of the bumpless pipe dreams called quantum bumpless pipe dreams, giving a combinatorial formula for quantum double Schubert polynomials as a sum of binomial weights of quantum bumpless pipe dreams. Finally, we will give a sketch for the proof of this formula.

For information about the Richard P. Stanley Seminar in Combinatorics, visit… https://math.mit.edu/combin/