On a Quantum Version of Pieri’s Formula

We give an algebro-combinatorial proof of a general version of Pieri’s formula following the approach developed by Fomin and Kirillov in the paper “Quadratic algebras, Dunkl elements, and Schubert calculus.” We prove several conjectures posed in their paper. As a consequence, a new proof of classical Pieri’s formula for cohomology of complex flag manifolds, and that of its analogue for quantum cohomology is obtained in this paper. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.