GRASSMANNIAN COSET MODELS AND UNITARY REPRESENTATIONS OF W

In this paper it is shown that the 2 {minus} d coset models SU(p + 1){sub N} {direct product} U(1) provide unitary representations of the chiral operator algebra W{sub {infinity}} in the large level (N {r arrow} {infinity}) limit, with central charge c = 2p. For p {ge}2, the corresponding field theories possess additional symmetries which given rise to a U(p) matrix generalization of W{sub {infinity}}, denoted by W{sub {infinity}}{sup p}. Its commutation relations are obtained in closed form for all values of p and W{sub {infinity}} is identified with the U(1) trace part of W{sub {infinity}}{sup p}. It is also shown that W{sub {infinity}}{sup p} at large p is associated with the algebra of symplectic diffeomorphisms in four dimensions.