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--- blog:2025-01-01 [2025/01/02 06:12] – pzhou
+++ blog:2025-01-01 [2025/01/02 07:23] (current) – pzhou
@@ Line 24: / Line 24: @@
 There are two models for infinite dimensional vector space where an operator acts locally nilpotently, one is $\d_x$ on $\C[x]$, another is $z\cdot$ on $\C[z,1/z] / \C[z]$. One can certainly take bundles over this. The second one seems more amicable.
-Question: if $z$ is an nilpotent endomorphism of $V$, and $W \In V$ is a subspace invariant under $z$,
+Question: if $z$ is an nilpotent endomorphism of $V$, and $W \In V$ is a subspace invariant under $z$, how do I know how large is $ker(z: V/W \to V/W)$? OK, not sure.
+In our case, for a generic element in $Y_n$, an generic element in $L_i$ takes $i$ step to die under action by $z$. I want to believe that, $L_i$ is just a lattice, no better and no worse than any other lattices in $\C[t,t^{-1}]^2$. This should be the best description. If that is the case, then $Y_n$ is an iterated $\P^1$-bundle. Let's see if that is true.
+Yes, that is true, see http://arxiv.org/abs/0710.3216v2 their second paper on $sl(m)$ case.
+So why did Cautis-Kamnitzer only deal with $sl(m)$? What's so hard about general case?