Consider a chevalley group a field $K$, with the right chevalley basis. Let $\alpha$ be a root. Let $x_{\alpha}(t)$ be the corresponding root space. Define $w_{\alpha}(t)=x_{\alpha}(t)x_{-\alpha}(-t^{-1})x_{\alpha}(t)$ then define $h_{\alpha}(t)=w_{\alpha}(t)w_{\alpha}(1)^{-1}$. Then chevalley proves in his exposition that the subgroup $H$ generated by the $h_{\alpha}(t)$ where $\alpha$ varies over the roots and $t$ varies over $K$ is isomorphic to the maximal torus.

But I don`t see this in the case of $Sp(4)$. Its Lie algebra is $C_2$. For example let $\alpha =e_1-e_2$ be the fundamental root. Then I take $x_{\alpha}(t)=1+t(E_{12}-E_{43})$. Then I get that $h_{\alpha}(t)$ is not a diagonal matrix. Where did I go wrong?

After Nick's comment my new question is

Does there exists a chevalley basis of $Sp(2n)$ such that the $h_{\alpha}(t)$ are diagonal matrices?

The chevalley basis I am using is in Cartar's book ' Simple groups of Lie type'. The definition of the root space that I am using is in the yale lectures of steinberg which is in math.ucla.edu/~rst/YaleNotes.pdf

Thanks for help in advance.