Quantum cohomology of Grassmannians modulo symmetries

Details Quantum cohomology of Grassmannians modulo symmetries Quantum cohomology of Grassmannians modulo symmetries

2002-11-04

arxiv.org/abs/math/0211052v1

Mathematics

Algebraic Geometry

11 pages, presented at the 2002 Fall AMS Eastern Section Meeting on ring structures in Schubert calculus,Northeastern Universi

Scientific paper

The quantum cohomology of Grassmannians exhibits two symmetries related to the quantum product, namely a \Bbb {Z}/n action and an involution related to complex conjugation. We construct a new ring by dividing out these symmetries in an ideal theoretic way and analyze its structure, which is shown to control the sum of all coefficients appearing in the product of cohomology classes. We derive a combinatorial formula for the sum of all Littlewood-Richardson coefficients appearing in the expansion of a product of two Schur polynomials.

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