Generalized q-W∞ constraints for the elliptic hermitian matrix model

We construct the generalized W1+∞ 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.