Instanton moduli spaces and $\mathscr W$-algebras

Abstract

We describe the (equivariant) intersection cohomology of certain moduli spaces ("framed Uhlenbeck spaces") together with some structures on them (such as e.g.\ the Poincaré pairing) in terms of representation theory of some vertex operator algebras ("$\mathscr W$-algebras").

117 pages; v2, 120 pages, definition of the inner product corrected; v3, 122 pages, definition of hyperbolic semi-smallness is added; v4, 124 pages, edited according to the referee's suggestion; v5, 122 pages, reformatted with smfart.cls so that numberings are the same as published version