BTL和CTL层次结构的附加对称性
The Additional Symmetries for the BTL and CTL Hierarchies
摘要：
Toda格（TL）族是由K.Ueno和K.Takasaki在\cite{uenotaksasai}中首先引入的，它推广了Toda格方程\cite{toda} .沿着E.日期，M。Jimbo，M. Kashiwara和T. Miwa \cite{DJKM}在KP层次上，K.Ueno和K.Takasaki在\cite{uenotaksasai}中发展了TL层次的理论：它的代数结构、线性化、双线性恒等式、$τ$函数等，并在\cite{uenotaksasai}中考虑了TL族的B型和C型类似物，即BTL族和CTL族，它们分别对应于无限维李代数$\textmd{o}(\infty)$和$\textmd{sp}(\infty)$。本文主要研究BTL和CTL族的附加对称性。
英文摘要：
The Toda lattice (TL) hierarchy was first introduced by K.Ueno and K.Takasaki in \cite{uenotaksasai} to generalize the Toda lattice equations\cite{toda}. Along the work of E. Date, M. Jimbo, M. Kashiwara and T. Miwa \cite{DJKM} on the KP hierarchy, K.Ueno and K.Takasaki in \cite{uenotaksasai} develop the theory for the TL hierarchy: its algebraic structure, the linearization, the bilinear identity, $τ$ function and so on. Also the analogues of the B and C types for the TL hierarchy, i.e. the BTL and CTL hierarchies, are considered in \cite{uenotaksasai}, which are corresponding to infinite dimensional Lie algebras $\textmd{o}(\infty)$ and $\textmd{sp}(\infty)$ respectively. In this paper, we will focus on the study of the additional symmetries for the BTL and CTL hierarchies.
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