I work through the paper *On branched coverings of some homogeneous space* of *Kim* and *Manivel* and I came across the definition of the canonical bundle of the Lagrangian Grassmannian $\mathbb{LG}_n$, the set of $n$-dimensional lagrangian subspaces of a $2n$-dimensional symplectic vector space. In the paper it is called 'a fact' that the canonical bundle $K_{\mathbb{LG}_n} = \mathcal{O}_{\mathbb{LG}_n}(-n-1)$, but I'm not able to verify it. Can someone help me in this?

Thanks in advance.

L. Kern. Thus I had to build a new one but no reputations = not able to answer in comments. But thanks for those quick answers, I think @Jason Starrs answer might help. $\endgroup$ – L_K666 Aug 17 '16 at 11:47