Functorial relationships between quantum cohomology of complete and partial flag varieties

Details Functorial relationships between quantum cohomology of complete and partial flag varieties Functorial relationships between quantum cohomology of complete and partial flag varieties

2010-07-09

arxiv.org/abs/1007.1683v1

Mathematics

Algebraic Geometry

41 pages. To appear in the Journal of Differential Geometry

Scientific paper

We give a natural filtration F on quantum cohomology QH(G/B) of G/B, which respects the quantum product structure. Its associated graded algebra is isomorphic to the tensor product of QH(G/P) and a corresponding graded algebra of QH(P/B) after localization. When the quantum parameter goes to zero, this specializes to the filtration on the classical cohomology H(G/B) from the Leray spectral sequence associated to the fibration P/B --> G/B --> G/P.

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