I study the book "Affine Hecke algebras and orthogonal polynomials" by I.G. Macdonald. He propose a formula in section $4.2$, especially formula $(4.2.9)$. This formula is the following:
$$T(w)f(Y)=\sum_{v\leq w}{f_v(Y)T(v)}$$
where $\leq$ is the Bruhat ordering. The author states that one can prove this by induction on $l(w)$ (the length function). I can prove the inductionstart for $l(w)=0$ and $l(w)=1$, but i come not further if I have to prove the inductionstep. Can someone help me?
Thank you very much.