Journal of the Ramanujan Mathematical Society

Volume 28A, Issue SPL, July – Special Issue 2013 pp. 149–190.

Generalized Schubert Calculus

Authors: Nora Ganter and Arun Ram
Author institution: Department of Mathematics and Statistics, University of Melbourne, Parkville VIC 3010 Australia

Summary: This paper is a survey of the study of the T-equivariant generalized cohomology of flag varieties using two models, the Borel model and the moment graph model. We study the differences between the Schubert classes and the Bott-Samelson classes. After setup of the general framework we compute, for classes of Schubert varieties of complex dimension ≤ 3 in rank 2 (including A2, B2, G2 and A1(1)), moment graph representatives, Pieri-Chevalley formulas and products of Schubert classes. These computations generalize the computations in equivariant K-theory for rank 2 cases which are given in Griffeth-Ram [GR].

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