W1+∞ constraints for the hermitian one-matrix model

Abstract

We construct the multi-variable realizations of the W1+∞ algebra such that they lead to the W1+∞ n-algebra. Based on our realizations of the W1+∞ algebra, we derive the W1+∞ constraints for the hermitian one-matrix model. The constraint operators yield not only the W1+∞ algebra but also the closed W1+∞ n-algebra. Keywords: Conformal and W Symmetry, Matrix models, n-algebra