Plethystic B-type KP and universal character hierarchies

摘要

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 plethystictype 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.