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- W4298851289 abstract "We relate the counting of rational curves intersecting Schubert varieties of the Grassmannian to the counting of certain non-intersecting lattice paths on the cylinder, so-called vicious and osculating walkers. These lattice paths form exactly solvable statistical mechanics models and are obtained from solutions to the Yang-Baxter equation. The eigenvectors of the transfer matrices of these models yield the idempotents of the Verlinde algebra of the gauged u(n)-WZNW model. The latter is known to be closely related to the small quantum cohomology ring of the Grassmannian. We establish further that the partition functions of the vicious and osculating walker model are given in terms of Postnikov's toric Schur functions and can be interpreted as generating functions for Gromov-Witten invariants." @default.
- W4298851289 created "2022-10-02" @default.
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- W4298851289 date "2012-04-18" @default.
- W4298851289 modified "2023-10-15" @default.
- W4298851289 title "Quantum cohomology via vicious and osculating walkers" @default.
- W4298851289 doi "https://doi.org/10.48550/arxiv.1204.4109" @default.
- W4298851289 hasPublicationYear "2012" @default.
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