Plethystic B-type KP and universal character hierarchies

In this paper, we firstly construct plethystic-type Fermions and define plethystic Boson–Fermion correspondence which is a generalization of the classical Boson–Fermion correspondence. Using the shifted tableau, we can define plethystic-type Schur-Q functions $$Q_\lambda ^\pi $$ from the plethystic-type Boson–Fermion correspondence, analogously to the way we get the Schur-Q functions $$Q_\lambda $$ from the classical Jacobi–Trudi formula. Then, as a generalization of BKP hierarchy, we construct the plethystic-type BKP hierarchy and obtain its tau functions. By a twisted coupled Jacobi–Trudi formula, we construct a plethystic B-type universal character and the corresponding integrable hierarchy which governs the plethystic B-type universal character.