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The quantum differential equation of the Hilbert scheme of points in the\n plane

2009/06/19 by Andreĭ Okounkov, Okounkov, Andrei, Rahul Pandharipande +1 · 1 citation
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Advanced Topics in Algebra #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.0906.3587

Abstract

We discuss here basic properties of the quantum differential equation of the\nHilbert scheme of points in the plane. Our emphasis is on intertwining\noperators (which shift equivariant parameters) and their applications. In\nparticular, we obtain an exact solution to the connection problem from the\nDonaldson-Thomas point q=0 to the Gromov-Witten point q=-1. The paper is an\nexpanded version of what was once the last Section of arXiv:math/0411210.\n

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