Extended plethystic vertex operators and plethystic universal characters

By means of plethystic-type fermions and plethystic-type boson–fermion correspondence, which is a generalization of the classical boson–fermion correspondence, we obtain a two-component twisted plethystic-type symmetric functions $S_{[\lambda,\mu]}^{(\alpha,\beta)}$ from an $(\alpha,\beta)$-type boson–fermion correspondence, similarly to how the universal character $S_{[\lambda,\mu]}$ is derived from the classical boson–fermion correspondence (the twisted Jacobi–Trudi formula). As a generalization of the universal character hierarchy, we then construct the $(\alpha,\beta)$-type plethystic universal character hierarchy that contains a series of nonlinear partial differential equations of infinite order, and obtain its tau functions and Plücker relations.