Reading on root systems and Weyl groups, unfortunately I am highly confused when it comes to the spin-groups (the two-fold universal cover of SO$(2n, \mathbb{C})$, realizable as a quotiënt in a Clifford algebra). Does anyone maybe know what the Weyl group is of the group spin$(2n, \mathbb{C}))$? Or what the root system is? (Then I might be able to deduce the Weyl-group!) Or maybe some reference where it is explained? Most books I've tried only deal with the group SO$(2n, \mathbb{C}))$.
Thanks!