  A number of finite algorithms for constructing representation theoretic data
from group multiplications in a finite group G have recently been shown to be
related to amplitudes for combinatoric topological strings (G-CTST) based on
Dijkgraaf-Witten theory of flat G-bundles on surfaces. We extend this result to
projective representations of G using twisted Dijkgraaf-Witten theory. New
algorithms for characters are described, based on handle creation operators and
minimal multiplicative generating subspaces for the centers of group algebras
and twisted group algebras. Such minimal generating subspaces are of interest
in connection with information theoretic aspects of the AdS/CFT correspondence.
For the untwisted case, we describe the integrality properties of certain
character sums and character power sums which follow from these constructive
G-CTST algorithms. These integer sums appear as residues of singularities in
G-CTST generating functions. S-duality of the combinatoric topological strings
motivates the definition of an inverse handle creation operator in the centers
of group algebras and twisted group algebras.
