Show that under the identification of b^* with b described in Section 5.6, the action of W on 𝔥^

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Step 1:u000ALetu0027s recall the identification of $u005Cmathfrak{h}^*$ with $u005Cmathfrak{h}$ described in Sec

Show that under the identification of $b^$ with $b$ described in Section 5.6, the action of $W$ on $\mathfrak{h}^$ (described in (5.16)) coincides with the adjoint action of $W$ on $\mathbf{b}$.