Description
Section 1. What groups are we talking about? G = A x) T with A diag in SL(3) and T the 3-cycle (x,y,z)
Section 2. Affine pieces of G-Hilb corr. to combinatorics (a) Leng partitions (b) trihedral boats
Section 3. (a) and (b) by computer algebra: Running my Magma code is a fun, easy do-it-yourself game:
follow the instructions on https:/homepages.warwick.ac.uk/~masda/McKay/tri
Section 4. Compute some affine pieces in the baby case A = V4 = mu2 + mu2 by generators and relations
(or as quiver moduli, somewhat implicitly).
My title says ideas, methods and open problems, not results or theorems.