MULTIPARAMETER GENERALIZED UNIVERSAL CHARACTERS AND MULTIPARAMETER GENERALIZED B-TYPE UNIVERSAL CHARACTERS

Abstract We construct the quantum fields presentation of the generalized universal character and the generalized B-type universal character, and by acting the quantum fields presentations to the constant 1, the generating functions are derived. Furthermore, we introduce two integrable systems known as the generalized UC (GUC) hierarchy and the generalized B-type UC (GBUC) hierarchy satisfied by the generalized universal character and the generalized B-type universal character, respectively. Based on infinite sequences of complex numbers, we further establish the multiparameter generalized universal character and the multiparameter generalized B-type universal character, which have been proved to be solutions of the GUC hierarchy and the GBUC hierarchy, respectively.