DECOMPOSITIONS OF BOSONIC MODULES OF LIE ALGEBRAS W1+∞ AND W1+∞(glN)

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A bosonic construction (with central charge c = 2) of Lie algebras W1+∞ and W1+∞ (glN), as well as the decompositions into irreducible modules are described. And for W1+∞, when restricted to its Virasoro subalgebra Vir, a bosonic construction and the same decomposition for Vir are obtained.
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