From r-Spin Intersection Numbers to Hodge Integrals

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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 GL(∞) group. Then, from a W₁₊∞ constraint of the partition function of r-spin intersection numbers, we get a W₁₊∞ constraint for the Hodge partition function. The W₁₊∞ constraint completely determines the Schur polynomials expansion of the Hodge partition function.