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We apply results from the geometry of nilpotent orbits and nilpotent Slodowyslices, together with modularity and asymptotic analysis of characters, toprove many new isomorphisms between affine W-algebras and affine Kac-Moodyvertex algebras and their finite extensions at specific admissible levels. Inparticular we identify many new collapsing levels for W-algebras.

Singularities of nilpotent Slodowy slices and collapsing levels of W-algebras