Variation on a theme of Solomon Original Research Article

Let W be a Coxeter group with degrees d1,…,dn. Solomon (1966) uses an inductive argument on the rank of W to prove the formula ∑w∈Wql(w) = Πi=1n (1 − qdi)(1 − q) where ℓ(w) denotes the minimum number of simple reflections required to express w. We provide a new proof of this fact using the theory of orbit harmonics developed in Garsia and Haiman (1992). At the same time, we give a brief review of some relevant classical results about finite reflection groups.