Folded fans and string functions

The folded fans $F\Psi$ describe the recursion properties for the weights of integrable highest weight modules $L^\mu$. Being considered simultaneously for the set of string functions $\sigma_s^\mu$ belonging to the fundamental Weyl chamber and corresponding to the same congruence class the system of recursion relations gives rise to an equation that connect the string functions and the power series depending on the multiplicities of the folded fan $F\Psi$ weights. We apply these equations to study the properties of string functions $\sigma_s^\mu$ associated to the integrable modules for affine Lie algebras. New important relations for string functions are thus obtained. The set of folded fans provides a compact and effective tool to study them. Bibl. – 7 titles.