On the cohomology of moduli spaces of (weighted) stable rational curves

We give a recursive algorithm for computing the character of the cohomology of the moduli space ${\text{Mmb}}_{0,n}$ of stable $n$-pointed genus zero curves as a representation of the symmetric group ${\text{Sg}}_n$ on $n$ letters. Using the algorithm we can show a formula for the maximum length of this character. Our main tool is connected to the moduli spaces of weighted stable curves introduced by Hassett.