• DOI:10.1090/S1056-3911-05-00419-4
• Corpus ID: 7531211

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}
}

• Chiu-Chu Melissa Liu, Kefeng Liu, Jian Zhou
• Published 3 August 2003
• Mathematics
• Journal of Algebraic Geometry

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 proof of the ELSV formula relating Hurwitz numbers and Hodge integrals: