Virasoro constraints and polynomial recursion for the linear Hodge integrals

@article{Guo2016VirasoroCA,
  title={Virasoro constraints and polynomial recursion for the linear Hodge integrals},
  author={Shuai Guo and Gehao Wang},
  journal={Letters in Mathematical Physics},
  year={2016},
  volume={107},
  pages={757-791}
}
The Hodge tau-function is a generating function for the linear Hodge integrals. It is also a tau-function of the KP hierarchy. In this paper, we first present the Virasoro constraints for the Hodge tau-function in the explicit form of the Virasoro equations. The expression of our Virasoro constraints is simply a linear combination of the Virasoro operators, where the coefficients are restored from a power series for the Lambert W function. Then, using this result, we deduce a simple version of… 
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