Geodesic
The combinatorial quantum cohomology ring of $G/B$
Journal of Algebraic Combinatorics, Tome 21 (2005) no. 3, pp. 331-349.

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Summary: A purely combinatorial construction of the quantum cohomology ring of the generalized flag manifold is presented. We show that the ring we construct is commutative, associative and satisfies the usual grading condition. By using results of our previous papers [12, 13], we obtain a presentation of this ring in terms of generators and relations, and formulas for quantum Giambelli polynomials. We show that these polynomials satisfy a certain orthogonality property, which-for $G = SL _{ n}( C {\cal C} )$-was proved previously in the paper [5].
Keywords: key words generalized flag manifolds, quantum cohomology, quantum Chevalley formula, quantum giambelli problem 
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     author = {Mare, Augustin-Liviu},
     title = {The combinatorial quantum cohomology ring of $G/B$},
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Mare, Augustin-Liviu. The combinatorial quantum cohomology ring of $G/B$. Journal of Algebraic Combinatorics, Tome 21 (2005) no. 3, pp. 331-349. http://geodesic.mathdoc.fr/item/JAC_2005__21_3_a1/