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

References in corpus (1)

• Dispersionless Hirota equations of two-component BKP hierarchy

Cited by in corpus (17)

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• The gauge transformation of the constrained semi-discrete KP hierarchy
• Toda lattice with constraint of type B
• BKP and CKP revisited: The odd KP system
• Kadomtsev-Petviashvili hierarchies of types B and C
• Quantum Torus symmetries of the CKP and multi-component CKP hierarchies
• BKP Hierarchy, Affine Coordinates, and a Formula for Connected Bosonic $N$-Point Functions
• Connected $(n,m)$-Point Functions of Diagonal $2$-BKP Tau-Functions, and Spin Double Hurwitz Numbers
• Elliptic solutions of the Toda lattice with constraint of type B and deformed Ruijsenaars-Schneider system
• Negative Generators of the Virasoro Constraints for the BKP Hierarchy
• Additional Symmetry of CKP hierarchy
• The applications of the gauge transformation for the BKP hierarchy
• Elliptic solutions of the semi-discrete BKP equation
• The integral type gauge transformation and the additional symmetry for the constrained KP hierarchy