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An Involution on the Quantum Cohomology Ring of the Grassmannian

Harald Hengelbrock
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Abstract

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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Harald Hengelbrock. 2002-05-24. An Involution on the Quantum Cohomology Ring of the Grassmannian. https://arxiv.org/abs/math/0205260

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