From r-spin intersection numbers to Hodge integrals

A bstract 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 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.