We construct the generalized W 1 + ∞ algebra with the multi-variable realization and derive its n -algebra which is the generalized Lie algebra for even n case. Then we reinvestigate the elliptic hermitian matrix model and present the generalized q - W ∞ constraints, where the abelian current operators are truncated. By applying the strategy of carrying out the action of the operators on the partition function, the generalized q - W ∞ n -algebra arises as a deformation of the generalized W ∞ n -algebra.
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