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Gromov–Witten Invariants of Flag Manifolds, VIA D ‐Modules
Author(s) -
Amarzaya A.,
Guest M. A.
Publication year - 2005
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610705006381
Subject(s) - generalized flag variety , flag (linear algebra) , mathematics , quantum cohomology , pure mathematics , axiom , cohomology , lie algebra , group (periodic table) , algebra over a field , lie group , equivariant cohomology , geometry , physics , quantum mechanics
We present a method for computing the 3‐point genus zero Gromov–Witten invariants of the complex flag manifold G / B from the relations of the small quantum cohomology algebra QH * G / B ( G is a complex semisimple Lie group and B is a Borel subgroup). In [ 3 ] and [ 9 ], at least in the case G = GL n C, two algebraic/combinatoric methods have been proposed, based on suitably designed axioms. Our method is quite different, being differential geometric in nature; it is based on the approach to quantum cohomology described in [ 7 ], which is in turn based on the integrable systems point of view of Dubrovin and Givental.