l-adic Cohomology groups of the grassmanian G(d, n)

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I'm trying to evaluate the cohomology groups of the grassmanian, I think $H^{n}(G(d, n), \mathbb{Q}_{l})$ should be trivial for $n$ odd, and that they are $\mathbb{Q}_{l}$ for $n$ even. Is this correct? does anyone know how to show it?