Folded fans and string functions

Abstract

Folded fans Fψ describe recursion properties of weights of integrable highest weight modules L u . Being considered simultaneously for the set of string functions $$ \sigma_s^u $$ belonging to a fundamental Weyl chamber and corresponding to the same congruence class, the system of recursion relations gives rise to an equation which connects the string functions and the power series depending on multiplicities of weights of a folded fan Fψ. We apply these equations to study properties of string functions $$ \sigma_s^u $$ associated with 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. Bibliography: 7 titles.