Reductions on B-type universal character hierarchy

Abstract

Basing on the universal character of B-type (BUC) hierarchy, through periodic reduction, we derived the bilinear equations that have the generalized reduced Schur Q-functions as tau functions. This process achieves a reduction of the BUC hierarchy. We refer to the resulting system as a reduced BUC hierarchy. Subsequently, the algebraic structure of the reduced BUC hierarchy is studied from the perspective of representation theory. We do this by transforming the bilinear equations using the neutral fermionic language. It is a widely accepted fact that a tau-function is considered as a solution of the BUC hierarchy when and only when it can be decomposed into a shifted action between two tau functions of the BKP hierarchy. We utilize this relationship to discover a class of polynomial tau-functions after the reduction of the BUC hierarchy. Furthermore, we extend our previous results to the B-type generalized UC (BGUC) hierarchy and its reduction.