Zhou's two-partition Hodge integral formula

From papers

Let Gμ+,μ(λ;τ)G^\bullet_{\mu^+,\mu^-}(\lambda;\tau) be the disconnected generating function of two-partition Hodge integrals for partitions μ+\mu^+ and μ\mu^-. Let Rμ+,μ(λ;τ)R^\bullet_{\mu^+,\mu^-}(\lambda;\tau) be the representation-theoretic expression formed from symmetric-group characters and the Hopf-link function Wμ+,μ(q)\mathcal{W}_{\mu^+,\mu^-}(q), where q=e1λq=e^{\sqrt{-1}\lambda}. Zhou's conjecture.

Gμ+,μ(λ;τ)=Rμ+,μ(λ;τ).G^\bullet_{\mu^+,\mu^-}(\lambda;\tau)=R^\bullet_{\mu^+,\mu^-}(\lambda;\tau).

This extends the one-partition formula to two partitions and relates two-partition Hodge integrals to the HOMFLY polynomial of the Hopf link. The source provides no evidence of resolution in the supplied material.

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Sources & referencesView supporting material

Primary source

Chiu-Chu Melissa Liu, “Formulae of one-partition and two-partition Hodge integrals”, arXiv:math/0502430 (2009).

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