Timeline for $D(\mathcal{O}(n))$ via generators and relations

8 events

when toggle format	what		by	license	comment
Nov 28, 2020 at 9:51	history	edited	Vas	CC BY-SA 4.0	added 1392 characters in body
Oct 26, 2020 at 11:27	comment	added	Simon Wadsley		It is still true that there is a surjective algebra map $U(\mathfrak{sl}(V))\to D(\mathbb{P}(V),\mathcal{O}(n))$ for essentially the same reason as for the full flag variety and the case $n=0$. However I don't know if there is a good description of generators of the kernel.
Oct 26, 2020 at 8:26	comment	added	Nicolas Hemelsoet		Yes, sorry I was too hasty.
Oct 25, 2020 at 23:03	comment	added	Vas		I would say that you get $U(\mathfrak{sl}(V))/\operatorname{ker}\chi_0$ if you consider global differential operators on the flag variety of $\mathfrak{sl}(V)$. But I am asking about differential operators on $\mathbb{P}(V)$ that is a certain partial flag variety of $\mathfrak{sl}(V)$.
Oct 25, 2020 at 22:40	comment	added	Nicolas Hemelsoet		If I am not mistaken, for $n=0$, this is $U(\mathfrak{sl}(V))/ (\ker \chi_0)$, where $\chi_0 : Z \to \Bbb C$ is the trivial character and $Z$ the center. But I am not sure how to write down the center in term of the usual Chevalley generators.
S Oct 25, 2020 at 22:32	history	suggested	Aurelio	CC BY-SA 4.0	Changed title to mathjax.
Oct 25, 2020 at 21:53	review	Suggested edits
S Oct 25, 2020 at 22:32
Oct 25, 2020 at 21:18	history	asked	Vas	CC BY-SA 4.0