The Q-deformed SUC, BUC hierarchies and the multi-component generalizations.

In this paper, we construct two kinds of q -differential integrable hierarchies. The first one is the q -universal character of B-type (BUC) and lattice q -BUC hierarchies expressed by q -shift operators. It is also shown that the lattice q -BUC hierarchy reduces to the q -BUC hierarchy with certain conditions. The other one is the q -deformed generalized symplectic Schur functions and the q -deformed generalized Q-functions defined by q -derivative operators. By means of the q -deformed vertex operators, the q -deformed symplectic universal character (SUC) and BUC hierarchies have been presented. Moreover, it is proved that q -deformed generalized symplectic Schur functions and generalized Q-functions are solutions of the q -deformed SUC and BUC hierarchies, respectively. Meanwhile, by using multi-component tau functions, we establish the multi-component q -deformed SUC and BUC hierarchies. In addition, based upon the discrete tau functions, the multi-component modified q -deformed SUC and BUC hierarchies have been discussed. [ABSTRACT FROM AUTHOR]