Many Boson Realizations of Universal Nonlinear $W_{\infty}$-Algebras

Details Many Boson Realizations of Universal Nonlinear $W_{\infty}$-Algebras Many Boson Realizations of Universal Nonlinear $W_{\infty}$-Algebras

1993-01-14

arxiv.org/abs/hep-th/9301053v1

Lett.Math.Phys. 29 (1993) 175-182

Physics

High Energy Physics

High Energy Physics - Theory

10p, (plain LaTex), Modified KP Hierarchies and Graded Lie Algebras

Scientific paper

An infinite number of free field realizations of the universal nonlinear $\hat{W}_{\infty}^{(N)}$ ($\hat{W}_{1+\infty}^{(N)}$) algebras, which are identical to the KP Hamiltonian structures, are obtained in terms of $p$ plus $q$ scalars of different signatures with $p-q=N$. They are generalizations of the Miura transformation, and naturally give rise to the modified KP hierarchies via corresponding realizations of the latter. Their characteristic Lie-algebraic origin is shown to be the graded $SL(p,q)$.

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