The additional symmetries for the BTL and CTL hierarchies

Abstract

In this paper, we construct the additional symmetries for the Toda lattice hierarchies of B type and C type (the BTL and CTL hierarchies), and show their algebraic structures are \documentclass[12pt]{minimal}\begin{document}$w_\infty ^B\times w_\infty ^B$\end{document}w∞B×w∞B and \documentclass[12pt]{minimal}\begin{document}$w_\infty ^C\times w_\infty ^C$\end{document}w∞C×w∞C , respectively. And also we discuss the generating functions of the additional symmetries.