The Additional Symmetries for the BTL and CTL Hierarchies

Abstract

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, $\tau$ 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 $\text{o}(\infty )$ and $\text{sp}(\infty )$ respectively. In this paper, we will focus on the study of the additional symmetries for the BTL and CTL hierarchies.

13 pages

References in corpus (2)

• On the BKP hierarchy: additional symmetries, Fay identity and Adler-Shiota-van Moerbeke formula
• On the String Equation of the BKP Hierarchy

Cited by in corpus (9)

• Block algebra in two-component BKP and D type Drinfeld-Sokolov hierarchies
• Virasoro type algebraic structure hidden in the constrained discrete KP hierarchy
• The compatibility of additional symmetry and gauge transformations for the constrained discrete Kadomtsev-Petviashvili hierarchy
• The gauge transformation of the constrained semi-discrete KP hierarchy
• Quantum torus algebras and B(C) type Toda systems
• On the squared eigenfunction symmetry of the Toda lattice hierarchy
• Squared Eigenfunction Symmetries for the BTL and CTL Hierarchies
• The applications of the gauge transformation for the BKP hierarchy
• The integral type gauge transformation and the additional symmetry for the constrained KP hierarchy