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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn073, 21 pages, doi:10.1093/imrp/rnn073 published on July 13, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

The Equivariant Gromov–Witten Theory of Formula and Integrable Hierarchies

Todor E. Milanov1

1 Mathematics Department, Stanford University, CA 94305, USA

Correspondence: Correspondence to be sent to: milanov_todor_e{at}yahoo.com

We construct an integrable hierarchy in terms of vertex operators and Hirota quadratic equations (HQE, in short) and we show that the equivariant total descendent potential of Formula satisfies the HQE. Our proof is based on the quantization formalism developed in Givental [5, 7] and on the equivariant mirror model of Formula We also show that under certain change of the variables, which is due to E. Getzler, the HQE are transformed into the HQE of the 2-Toda hierarchy. Thus, we obtain a new proof of the equivariant Toda conjecture.



References

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This Article
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