Title: Character formulas on cohomology of deformations of Hilbert schemes of<i>K</i>3 surfaces
Abstract: Let X be a hyperkähler manifold deformation equivalent to a Hilbert scheme of n points on a K 3 surface. We compute the graded character formula of the generic Mumford–Tate group representation on the cohomology ring of X, and derive a generating series for deducing the number of canonical Hodge classes on X. The formula indicates the number of Hodge classes on X that remain Hodge under any deformation.