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Jun 23, 2022 at 20:59 comment added andrewBee For type A, see Fulton's Young Tableaux, Chapter 9.
Jun 23, 2022 at 16:28 comment added abx No, except for \emph{minimal} flag varieties (e.g. Grassmannians): as soon as $\operatorname{rk}\operatorname{Pic}(V)>1 $, the homogeneous coordinate ring of $V$ is not a UFD. See Hartshorne, exer. II.6.3.c).
Jun 23, 2022 at 16:04 history asked F.H.A CC BY-SA 4.0