Quantum torus algebras and B(C) type Toda systems

Abstract

In this paper, we construct a new even constrained B(C) type Toda hierarchy and derive its B(C) type Block type additional symmetry. Also we generalize the B(C) type Toda hierarchy to the $N$-component B(C) type Toda hierarchy which is proved to have symmetries of a coupled ${⨂}^{N}Q{T}_{+}$ algebra ( $N$-folds direct product of the positive half of the quantum torus algebra $QT$).

arXiv comment13 Pages, accepted for publication in the Journal of Nonlinear Science

References in corpus (10)

• Multiple orthogonal polynomials of mixed type: Gauss-Borel factorization and the multi-component 2D Toda hierarchy
• Block type symmetry of bigraded Toda Hierarchy
• Tau function and Hirota bilinear equations for the Extended bigraded Toda Hierarchy
• The extended $Z_N$-Toda hierarchy
• Dispersionless bigraded Toda Hierarchy and its additional symmetry
• Solutions of bigraded Toda hierarchy
• The multicomponent 2D Toda hierarchy: Discrete flows and string equations
• On the extended multi-component Toda hierarchy
• Hirota equations for the extended bigraded Toda hierarchy and the total descendent potential of CP^1 orbifolds
• The Additional Symmetries for the BTL and CTL Hierarchies

Cited by in corpus (2)

• The Cauchy two-matrix model, C-Toda lattice and CKP hierarchy
• Quantum torus symmetries of multicomponent modified KP hierarchy and reductions