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7
votes
Accepted
Beilinson-Bernstein localization: $\mathfrak{g}$ action on $G$-equivariant sheaf
Here, $\gamma(h)^*$ means applying the isomorphism $\gamma(h)^*\colon \mathcal{L}_{\gamma(h)\cdot x}\to\mathcal{L}_x$ which comes from the equivariant structure. … For functions (and the usual equivariant structure), this is just identifying $\mathbb{C}\cong \mathbb{C}$ by the identity, so this includes the formula above. …
1
vote
Do fixed point sets in equivariant crepant resolutions have the same cohomology? How about ...
If the $\mathbb{C}^*$ of interest to you comes from a linear action of the cotangent bundle you reduced to get the quiver variety, then you can make the diffeomorphism $S^1$-equivariant, and thus induce …