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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.