arXiv subjects
Publications and source records attributed to Zhao-Wen Yan.
We present the $W_{1+\infty}$ constraints for the Gaussian Hermitian matrix model, where the constructed constraint operators yield the $W_{1+\infty}$ $n$-algebra. For the Virasoro constraints, we note that the constraint operators give the null 3-algebra. With the help of our Virasoro constraints, we derive a new effective formula for correlators in the Gaussian Hermitian matrix model.
We construct the multi-variable realizations of the $W_{1+\infty}$ algebra such that they lead to the $W_{1+\infty}$ $n$-algebra. Based on our realizations of the $W_{1+\infty}$ algebra, we derive the $W_{1+\infty}$ constraints for the hermitian one-matrix model. The constraint operators yield not only the $W_{1+\infty}$ algebra but also the closed $W_{1+\infty}$ $n$-algebra.
We present the nontrivial $W_{1+\infty}$ $n$-algebra and analyze its remarkable properties. We investigate the $W_{1+\infty}$ $n$-algebra in the Landau problem and discuss the realization of the classical $w_{\infty}$ 3-algebra. Furthermore, we discuss the case of the many-body system in the lowest Landau level and derive the constraints for correlation functions of the vertex operators.
We investigate the quantum Calogero-Moser model and reveal its hidden symmetries, i.e., the $W_{1+\infty}$ and Virasoro-Witt 3-algebras. In the large $N$ limit, we note that these two infinite dimensional 3-algebras reduce to the $w_{\infty}$ and special Virasoro-Witt 3-algebras which satisfy the fundamental identity condition, respectively.
n-ary algebras have played important roles in mathematics and mathematical physics. The purpose of this paper is to construct a deformation of Virasoro-Witt n-algebra based on an oscillator realization with two independent parameters (p, q) and investigate its n-Lie subalgebra.
The $q$-deformation of the infinite-dimensional $n$-algebra is investigated. Based on the structure of the $q$-deformed Virasoro-Witt algebra, we derive a nontrivial $q$-deformed Virasoro-Witt $n$-algebra which is nothing but a sh-$n$-Lie algebra. Furthermore in terms of the pseud-differential operators on the quantum plane, we construct the (co)sine $n$-algebra and the $q$-deformed $SDiff(T^2)$ $n$-algebra. We prove that they are the sh-$n$-Lie algebras for the case of even $n$. An explicit physical realization of the (co)sine $n$-algebra is given.