Mariño-Vafa formula and Hodge integral identities

@article{Liu2003MarioVafaFA,
  title={Mari{\~n}o-Vafa formula and Hodge integral identities},
  author={Chiu-Chu Melissa Liu and Kefeng Liu and Jian Zhou},
  journal={Journal of Algebraic Geometry},
  year={2003},
  volume={15},
  pages={379-398}
}
Based on string duality Marino and Vafa [10] conjectured a closed formula on certain Hodge integrals in terms of representations of symmetric groups. This formula was first explicitly written down by the third author in [13] and proved in joint work [8] of the authors of the present paper. For a different approach see [12]. Our proof follows the strategy of proving both sides of the equation satisfy the same cut-and-join equation and have the same initial values. In this note we will describe a… 
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References

SHOWING 1-10 OF 26 REFERENCES
Hodge Integrals and Hurwitz Numbers via Virtual Localization
We give another proof of Ekedahl, Lando, Shapiro, and Vainshtein's remarkable formula expressing Hurwitz numbers (counting covers of P1 with specified simple branch points, and specified branching
Hodge integrals and invariants of the unknot
We prove the Gopakumar{Mari~ no{Vafa formula for special cubic Hodge integrals. The GMV formula arises from Chern{Simons/string duality applied to the unknot in the three sphere. The GMV formula is a
Virasoro constraints and the Chern classes of the Hodge bundle
Hodge integrals and Gromov-Witten theory
Integrals of the Chern classes of the Hodge bundle in Gromov-Witten theory are studied. We find a universal system of differential equations which determines the generating function of these
GROMOV - WITTEN INVARIANTS AND QUANTIZATION OF QUADRATIC HAMILTONIANS
We describea formalism based on quantizationof quadratichamil- tonians and symplectic actions of loop groups which provides a convenient home for most of known general results and conjectures about
Virasoro constraints for target curves
We prove generalized Virasoro constraints for the relative Gromov-Witten theories of all nonsingular target curves. Descendents of the even cohomology classes are studied first by localization,
Symplectic surgery and Gromov-Witten invariants of Calabi-Yau 3-folds
We define relative Gromov-Witten invariants and establish a general gluing theory of pseudo-holomorphic curves for symplectic cutting and contact surgery. Then, we use our general gluing theory to
Hodge integrals, partition matrices, and the λ g conjecture
We prove a closed formula for integrals of the cotangent line classes against the top Chern class of the Hodge bundle on the moduli space of stable pointed curves. These integrals are computed via
Relative Gromov-Witten invariants
We define relative Gromov-Witten invariants of a symplectic manifold relative to a codimension-two symplectic submanifold. These invariants are the key ingredients in the symplectic sum formula of
The symplectic sum formula for Gromov–Witten invariants
In the symplectic category there is a 'connect sum' operation that glues symplectic manifolds by identifying neighborhoods of embedded codimension two submanifolds. This paper establishes a formula
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