Abstract
Generalized Kontsevich Matrix Model (GKMM) with a certain given potential is the partition function of r-spin intersection numbers. We represent this GKMM in terms of fermions and expand it in terms of the Schur polynomials by boson-fermion correspondence, and link it with a Hurwitz partition function and a Hodge partition by operators in a \( \widehat{GL}\left(\infty \right) \) group. Then, from a W 1+∞ constraint of the partition function of r-spin intersection numbers, we get a W 1+∞ constraint for the Hodge partition function. The W 1+∞ constraint completely determines the Schur polynomials expansion of the Hodge partition function.
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Ding, XM., Li, Y. & Meng, L. From r-spin intersection numbers to Hodge integrals. J. High Energ. Phys. 2016, 15 (2016). https://doi.org/10.1007/JHEP01(2016)015
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DOI: https://doi.org/10.1007/JHEP01(2016)015