Combinatoric topological string theories and group theory algorithms

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