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--- blog:2024-01-05 [2024/01/06 08:25] – pzhou
+++ blog:2024-01-05 [2024/01/07 01:04] (current) – pzhou
@@ Line 1: / Line 1: @@
 ====== 2024-01-05 ======
-In the simplest setting, we have mirror symmetry for $\Coh(\C^* \times \C^2)$.
+In the simplest setting, we have mirror symmetry for $Coh(\C^* \times \C^2)$.
 Next, we are going to take symmetric power.
-Do you remember what happens when two eigenvalues collide? No, don't do Hermitian matrices, that will never be nilpotent.
+Do you remember what happens when two eigenvalues collide? No, don't do Hermitian matrices, that will never be nilpotent. What if you have a matrix that looks like $( (1,1), (0, 1+x) )$. What is the eigenvector for e.v. $1+x$? How about $(1,x)$? Eigenvector for $\lambda = 1$, is $(1,0)$. So you see, when $x \to 0$, the two eigenspaces also collide!
+The key question is: what is the superKLRW algebra?
+From the A-side, let me guess, we have 'fiber product' of two MC. So, when y1 = y2, in the fiber, we need to have x1 = x2, and z1 = z2 (the new pair of fiber coord). And we need to remember the ratio of (x1-x2)/(y1-y2), and (z1-z2)/(y1-y2).
-What if you have a matrix that looks like $( (1,1), (0, 1+x) )$. What is the eigenvector for e.v. $1+x$? How about $(1,x)$? Eigenvector for $\lambda = 1$, is $(1,0)$. So you see, when $x \to 0$, the two eigenspaces also collide!