  The equivariant cohomology of certain moduli spaces of sheaves on isotrivial
elliptic surfaces are shown to admit representations of infinite dimensional
Lie (super)algebras. The construction is based on work of Billig and
Chen-Li-Tan on vertex representations of toroidal extended affine Lie algebras,
and a geometric interpretation of bc-ghost systems on Hilbert schemes of points
on ruled surfaces. The role of higher-nullity toroidal extended affine lie
algebras are discussed in relation to tensor products of modules of a
Yangian-like associative algebra. Applications to enumerative geometry are
discussed in the introduction.
