I want to know what are the holomorphic automorphisms of a Grassmannian. Can someone tell me this?
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2$\begingroup$ ams.org/journals/proc/198910601/S00029939198909389098 $\endgroup$– Carlo BeenakkerJul 1, 2014 at 6:29

1$\begingroup$ @Carlo: I suggest that you promote your comment to an answer. $\endgroup$– Neil StricklandJul 1, 2014 at 8:17

5$\begingroup$ It probably would have been a good idea to quote the paper by WeiLiang Chow, On the geometry of algebraic homogeneous spaces, Ann. of Math. 50 (1949), 32–67, since that is where the original argument is made. $\endgroup$– Robert BryantJul 1, 2014 at 16:17
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$\begingroup$ @Mostafa  see section 2 of Cowen's paper for the construction of the dual map. $\endgroup$ Jul 1, 2014 at 9:51

6$\begingroup$ Demazure also gave a complete characterization of automorphism groups of generalized Grassmannians $G/P$, "Automorphismes et deformations des varietes de Borel", Invent. Math. 1977. Essentially, the automorphism group of $G/P$ is generated by $G$ (adjoint form) together with certain automorphisms of the Dynkin diagram. The above is a special case, since $Gr(k,n) = PGL_n/P$. $\endgroup$ Jul 1, 2014 at 14:02