Generalized Schubert Calculus
Representation Theory
2014-06-30 v1 Combinatorics
K-Theory and Homology
Abstract
In this paper we study 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 <4 in rank 2 (including A_2, B_2, G_2 and A_1^{(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 arXiv:math/0405333.
Cite
@article{arxiv.1212.5742,
title = {Generalized Schubert Calculus},
author = {Nora Ganter and Arun Ram},
journal= {arXiv preprint arXiv:1212.5742},
year = {2014}
}