W_{1+\infty} and W(gl_N) with central charge N

@article{Frenkel1994W\_1inftyAW,
  title={W\_\{1+\infty\} and W(gl\_N) with central charge N},
  author={Edward Vladimir Frenkel and Victor G. Kac and Andrey Radul and W. Wang},
  journal={arXiv: High Energy Physics - Theory},
  year={1994}
}
We study representations of the central extension of the Lie algebra of differential operators on the circle, the W-infinity algebra. We obtain complete and specialized character formulas for a large class of representations, which we call primitive; these include all quasi-finite irreducible unitary representations. We show that any primitive representation with central charge N has a canonical structure of an irreducible representation of the W-algebra W(gl_N) with the same central charge and… 
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