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# On a new proof of the Okuyama--Sakai conjecture

Mar 2023

In [40] Okuyama and Sakai gave a conjectural equality for the higher genusgeneralized Br\'ezin--Gross--Witten (BGW) free energies. In a recent work [45]we established the Hodge-BGW correspondence on the relationship between certainspecial cubic Hodge integrals and the generalized BGW correlators, and a proofof the Okuyama--Sakai conjecture was also given ${\it ibid}$. In this paper, wegive a new proof of the Okuyama--Sakai conjecture by a further application ofthe Dubrovin--Zhang theory for the KdV hierarchy.

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