An Involution on the Quantum Cohomology Ring of the Grassmannian

Details An Involution on the Quantum Cohomology Ring of the Grassmannian An Involution on the Quantum Cohomology Ring of the Grassmannian

2002-05-24

arxiv.org/abs/math/0205260v1

Mathematics

Algebraic Geometry

6 Pages, 1 figure

Scientific paper

For a Fano manifold M, complex conjugation defines a real involution on the quantum cohomology ring. For the Grassmannian we identify this involution with an explicit transformation on Schubert classes defined over the integers. It is a composition of a power of the cyclic action recently defined by Agnihotri and Woodward with Poincare duality. The existence of the involution has been observed independently and from a different point of view by Postnikov (math.CO/0205165).

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