Abstract
It is shown that the 2 – d coset models SU (p + 1)N/ SU (p)N ⊗ U (1) provide unitary representations of the chiral operator algebra W∞ in the large level (N → ∞) limit, with central charge c = 2p. For p ≥ 2, the corresponding field theories possess additional symmetries which given rise to a U (p) matrix generalization of W∞, denoted by [Formula: see text]. Its commutation relations are obtained in closed form for all values of p and W∞ is identified with the U(1) trace part of [Formula: see text]. It is also shown that [Formula: see text] at large p is associated with the algebra of symplectic diffeomorphisms in four dimensions.
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