Lecture Notes on Quantum Cohomology of the Flag Manifold


Sergey Fomin


This is an exposition of some recent developments related to the object in the title, particularly the computation of the Gromov-Witten invariants of the flag manifold [5] and the quadratic algebra approach [6]. The notes are largely based on the papers [5] and [6], authored jointly with S.~Gelfand, A.~N.~Kirillov, and A.~Postnikov. This is by no means an exhaustive survey of the subject, but rather a casual introduction to its combinatorial aspects.