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Let $\mathfrak g = \mathfrak g_0 \oplus \mathfrak g_1$ be a basic classical Lie super algebra and let $\rho = \text{half sum of even positive roots} - \text{half sum of odd positive roots}$ be the Weyl vector of $\mathfrak g$.

Let $W$ be the weyl group of $\mathfrak g_0$. For $w \in W$, how to calculate $w \cdot \rho$.

I am just confused about the action of $W$ on the odd roots.

Thank you.

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