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Nov 6, 2022 at 5:28 comment added Malkoun I should also mention that after reading parts of Seshadri's book, I found some nice slides by Leonard Hardiman to be helpful, because they had some figures (math.univ-lyon1.fr/~hardiman/hardiman_slides_C.pdf). I guess I need some figures to understand what the path operators are doing. I found this very helpful.
Nov 6, 2022 at 5:25 comment added Malkoun Thank you Sam Hopkins for mentioning Seshadri's book. It was really helpful to me, especially the fact that for the special cases studied there (which include $G/P$ with $P$ being a maximal parabolic subgroup), they index the basis using admissible pairs in $W/W_P$, where $W$ is the Weyl group and $W_P$ is the Weyl group of $P$. I found that interesting.
Oct 22, 2022 at 22:27 comment added Malkoun Thank you @RichardStanley and TimothyChow for your additional help ! I now have enough reading material. Seshadri's book, by the way, at least at the beginning, is easy-to-read, which is great. Thank you all!
Oct 22, 2022 at 12:38 comment added Timothy Chow In case Springer changes its URLs in the future, the paper mentioned in Richard Stanley's comment is The Development of Standard Monomial Theory-I by C. Musili, in A Tribute to C. S. Seshadri, pages 385–420.
Oct 22, 2022 at 2:59 comment added Richard Stanley The paper link.springer.com/chapter/10.1007/978-93-86279-11-8_24 and the book Hodge Algebras by DeConcini, Eisenbud, and Procesi may be of interest.
Oct 21, 2022 at 20:41 vote accept Malkoun
Oct 21, 2022 at 18:51 history answered Sam Hopkins CC BY-SA 4.0