A centerless Virasoro algebra of master symmetries for the Ablowitz-Ladik hierarchy

Details A centerless Virasoro algebra of master symmetries for the Ablowitz-Ladik hierarchy A centerless Virasoro algebra of master symmetries for the Ablowitz-Ladik hierarchy

2011-08-17

arxiv.org/abs/1108.3587v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

49 pages

Scientific paper

We show that the Ablowitz-Ladik hierarchy admits a centerless Virasoro algebra of master symmetries in the sense of Fuchssteiner. An explicit expression for these symmetries is given in terms of a generalization of the Cantero, Moral and Vel\'azquez (CMV) matrices (which can also be used to formulate the hierarchy itself) and their action on the tau-functions of the hierarchy is described. The use of the CMV matrices, in contrast with Hessenberg matrices, turns out to be crucial for obtaining a Lax pair representation of the master symmetries. As an application, a new and transparent derivation of the Virasoro constraints satisfied by the unitary matrix model is presented.

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