The Symmetric Function h^0(\bar{M}_{0,n}, L_1^{x_1} \tensor...\tensor L_n^{x_n})

Abstract

Let \bar{M}_{0,n} be the moduli space of pointed, genus 0 curves. Let L_i denote the line bundle on \bar{M}_{0,n} associated to the i-th marked point (the fiber of L_i is the cotangent space of the pointed curve at the i-th point). Y_n=h^0(\bar{M}_{0,n}, L_1^{x_1} \tensor... \tensor L_n^{x_n}) is a symmetric function of the variables x_1,... x_n. Let R be the ring of symmetric functions in infinitely many variables. An explicit linear transformation T: R-> R is found such that Y_n= T^{n-3} (1).