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The equivariant Gromov-Witten theory of P^1

Andrei Okounkov·Rahul Pandharipande
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Abstract

We express all equivariant Gromov-Witten invariants of the projective line as matrix elements of explicit operators acting in the Fock space. As a consequence, we prove the equivariant theory is governed by the 2-Toda hierarchy of Ueno and Takasaki. This is the second in a sequence of three papers devoted to the Gromov-Witten theory of nonsingular target curves (the first paper of the series is math.AG/0204305).

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Andrei Okounkov, Rahul Pandharipande. 2002-07-25. The equivariant Gromov-Witten theory of P^1. https://arxiv.org/abs/math/0207233

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