From Additional Symmetries to Linearization of Virasoro Symmetries

Abstract

We construct the additional symmetries and derive the Adler-Shiota-van Moerbeke formula for the two-component BKP hierarchy. We also show that the Drinfeld-Sokolov hierarchies of type D, which are reduced from the two-component BKP hierarchy, possess symmetries written as the action of a series of linear Virasoro operators on the tau function. It results in that the Drinfeld-Sokolov hierarchies of type D coincide with Dubrovin and Zhang's hierarchies associated to the Frobenius manifolds for Coxeter groups of type D, and that every solution of such a hierarchy together with the string equation is annihilated by certain combinations of the Virasoro operators and the time derivations of the hierarchy.

22 pages

References in corpus (1)

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

Cited by in corpus (9)

• Block algebra in two-component BKP and D type Drinfeld-Sokolov hierarchies
• Supersymmetric BKP systems and their symmetries
• Tau function of the CKP hierarchy and non-linearizable Virasoro symmetries
• Block (or Hamiltonian) Lie symmetry of dispersionless D type Drinfeld-Sokolov hierarchy
• ANITA: An Optimal Loopless Accelerated Variance-Reduced Gradient Method
• Bilinear equation and additional symmetries for an extension of the Kadomtsev-Petviashvili hierarchy
• Tau Functions and Virasoro Symmetries for Drinfeld-Sokolov Hierarchies
• The (n,1)-Reduced DKP Hierarchy, the String Equation and W Constraints
• Addition formulae of discrete KP, q-KP and two-component BKP systems