  We represent in the universal form restricted one-instanton partition
function of supersymmetric Yang-Mills theory. It is based on the derivation of
universal expressions for quantum dimensions (universal characters) of Cartan
powers of adjoint and some other series of irreps of simple Lie algebras. These
formulae also provide a proof of formulae for universal quantum dimensions for
low-dimensional representations, needed in derivation of universal knot
polynomials (i.e. colored Wilson averages of Chern-Simons theory on 3d sphere).
As a check of the (complicated) formulae for universal quantum dimensions we
prove numerically Deligne's hypothesis on universal characters for symmetric
cube of adjoint representation.
