(2,1)-type and (3)-type universal character hierarchies and the τ functions

This paper focuses on the construction of vertex operators of generalized (2,1)-type and (3)-type universal characters. On the basis of the generalized Hamiltonian with partitions [Formula: see text] and [Formula: see text], these two types of generalized universal characters are expressed as the expectation values. Moreover, based on the bilinear identities, the generalized (2,1)-type and (3)-type universal character hierarchies have been established whose [Formula: see text] functions are generalized (2,1)-type universal characters and generalized (3)-type universal characters, respectively.