# action of Weyl group element on Weyl vector

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.