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• CommentRowNumber1.
• CommentAuthorDavid_Corfield
• CommentTimeApr 17th 2018

I added references to John Baez’s two blog posts on The Geometric McKay Correspondence, Part I, Part II.

I hadn’t realised the length of legs in the Dynkin diagrams corresponds to the stabilizer order on vertices, edges, faces in the corresponding Platonic solid. So 2,3,5 for $E_8$ and the icosahedron.

• CommentRowNumber2.
• CommentAuthorDavid_Corfield
• CommentTimeMay 8th 2018

I added mention of Gonzalez-Sprinberg and J.-L. Verdier’s K-theoretic interpretation as discussed in the ’The McKay correspondence as an equivalence of derived categories’.

• CommentRowNumber3.
• CommentAuthorDavid_Corfield
• CommentTimeMay 9th 2018

If the comparison is between equivariant K-theory of $\mathbb{C}^2$ and ordinary K-theory of $\mathbb{C}^2/G$, is that an Elmendorf-theorem situation?

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeMay 9th 2018

Haven’t looked yet at the article that you are looking at, but Elmendorf’s theorem is about restricting to fixed points, not about passing to quotients (not manifestly and directly, at least).

• CommentRowNumber5.
• CommentAuthorDavid_Corfield
• CommentTimeMay 9th 2018

I was drawing on the Bridgeland et al. article for that K-theoretic description, which they propose to generalise to

G-equivariant K theory of M [=X/G] and the ordinary K theory of a crepant resolution Y of X,

But, as you say, I guess that’s not about fixed points.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeMay 9th 2018

Thanks for the pointer. Interesting.

But, yes, that old trick with those du Val resolutions is presently not related, beyond the general context, to the perspective through Elmendorf’s theorem. I wish I knew how to make an tighter connection between the two.