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Flag varieties and Schubert calculus. (English) Zbl 1121.14303
Tschinkel, Yuri (ed.), Algebraic groups. Proceedings of the summer school, Georg-August-Universität zu Göttingen, Göttingen, Germany, June 27–July 13, 2005. Göttingen: Universitätsverlag Göttingen (ISBN 978-3-938616-77-2/pbk). Universitätsdrucke Göttingen. Seminare/Mathematisches Institut, 73-86 (2007).
The author gives a brief survey on developments in Schubert calculus. Starting with the very foundations of intersection theory on Grassmannians, including the classical Schubert calculus and combinatorial results like the Pieri and the Giambelli formula, he proceeds with flag varieties and the extension of Schubert calculus by quantum cohomology. He describes approaches to recent proofs of general Littlewood-Richardson rules and gives several examples.
For the entire collection see [Zbl 1117.11004].

14N15 Classical problems, Schubert calculus
14M15 Grassmannians, Schubert varieties, flag manifolds