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(2010 / vol.12 / no.1)
Schubert calculus, seen from torus equivariant topology
Shizuo KAJI
Pages. 71-89   



We survey the classical (ordinary) Schubert calculus in the first half of this note.
Then we lift everything up to an equivariant setting;
we see three descriptions of the equivariant cohomology of flag varieties
and investigate their relation.
The example given in S
ef{example} will be helpful to read this note.
end{abstract}



1. Introduction: Schubert's quiz
2. What is Schubert calculus
3. Schubert calculus in Bott tower
4. Schubert polynomials
5. Equivariant cohomology of flag varieties
6. Left $W imes W$-action on $H^*_T(G/B;)$
7. Divided difference operators
8. Reduction to the ordinary cohomology
9. Some open problems
10. Example
11. Further readings



equivariant cohomology, flag variety, Schubert calculus, GKM theory



57T15; 14M15