On the BKP hierarchy: additional symmetries, Fay identity and Adler-Shiota-van Moerbeke formula

Abstract

We give an alternative proof of the Adler-Shiota-van Moerbeke formula for the BKP hierarchy. The proof is based on a simple expression for the generator of additional symmetries and the Fay identity of the BKP hierarchy.

14 pages

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Cited by in corpus (34)

• Block type symmetry of bigraded Toda Hierarchy
• Additional symmetries of constrained CKP and BKP hierarchies
• Elliptic solutions to integrable nonlinear equations and many-body systems
• Gauge transformation and symmetries of the commutative multi-component BKP hierarchy
• Supersymmetric BKP systems and their symmetries
• From Additional Symmetries to Linearization of Virasoro Symmetries
• The "Ghost" Symmetry of the BKP hierarchy
• Quantum Torus symmetry of the KP, KdV and BKP hierarchies
• Tau function of the CKP hierarchy and non-linearizable Virasoro symmetries
• Bilinear equations in Darboux transformations by Boson-Fermion correspondence
• The "ghost" symmetry in the CKP hierarchy
• Dynamics of poles of elliptic solutions to the BKP equation
• The Additional Symmetries for the BTL and CTL 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
• On the String Equation of the BKP Hierarchy
• Toda lattice with constraint of type B
• BKP and CKP revisited: The odd KP system
• Kadomtsev-Petviashvili hierarchies of types B and C
• Dispersionless and multicomponent BKP hierarchies with quantum torus symmetries
• The wronskian solution of the constrained discrete KP hierarchy
• Quantum Torus symmetries of the CKP and multi-component CKP hierarchies
• BKP Hierarchy, Affine Coordinates, and a Formula for Connected Bosonic $N$-Point Functions
• On the squared eigenfunction symmetry of the Toda lattice hierarchy
• Elliptic solutions of the Toda lattice with constraint of type B and deformed Ruijsenaars-Schneider system
• Connected $(n,m)$-Point Functions of Diagonal $2$-BKP Tau-Functions, and Spin Double Hurwitz Numbers
• The Recursion operators of the BKP hierarchy and the CKP Hierarchy
• Negative Generators of the Virasoro Constraints for the BKP Hierarchy
• Additional symmetry of the modified extended Toda hierarchy
• The applications of the gauge transformation for the BKP hierarchy
• The integral type gauge transformation and the additional symmetry for the constrained KP hierarchy
• Additional Symmetry of CKP hierarchy
• Elliptic solutions of the semi-discrete BKP equation