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arXiv · 0810.0981

Quantum K-theory of Grassmannians

Anders S. Buch·Leonardo C. Mihalcea
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Abstract

We show that (equivariant) K-theoretic 3-point Gromov-Witten invariants of genus zero on a Grassmann variety are equal to triple intersections computed in the ordinary (equivariant) K-theory of a two-step flag manifold, thus generalizing an earlier result of Buch, Kresch, and Tamvakis. In the process we show that the Gromov-Witten variety of curves passing through 3 general points is irreducible and rational. Our applications include Pieri and Giambelli formulas for the quantum K-theory ring of a Grassmannian, which determine the multiplication in this ring. Our formula for Gromov-Witten invariants can be partially generalized to cominuscule homogeneous spaces by using a construction of Chaput, Manivel, and Perrin.

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Anders S. Buch, Leonardo C. Mihalcea. 2008-10-06. Quantum K-theory of Grassmannians. https://doi.org/10.1215/00127094-2010-218

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