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15 February 2011 Quantum K-theory of Grassmannians
Anders S. Buch, Leonardo C. Mihalcea
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Duke Math. J. 156(3): 501-538 (15 February 2011). DOI: 10.1215/00127094-2010-218

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 (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 three 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. We also compute the dual Schubert basis for this ring and show that its structure constants satisfy S3-symmetry. 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. "Quantum K-theory of Grassmannians." Duke Math. J. 156 (3) 501 - 538, 15 February 2011. https://doi.org/10.1215/00127094-2010-218

Information

Published: 15 February 2011
First available in Project Euclid: 9 February 2011

zbMATH: 1213.14103
MathSciNet: MR2772069
Digital Object Identifier: 10.1215/00127094-2010-218

Subjects:
Primary: 14N35
Secondary: 14E08 , 14M15 , 14N15 , 19E08

Rights: Copyright © 2011 Duke University Press

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Vol.156 • No. 3 • 15 February 2011
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