Quasifinite representations of W_{\infty}

Details Quasifinite representations of W_{\infty} Quasifinite representations of W_{\infty}

1999-10-29

arxiv.org/abs/math/9910172v1

Mathematics

Quantum Algebra

Amstex, 18 pages

Scientific paper

We classify the quasifinite highest weight modules over a family of subalgebras W_{\infty}^{n} of the central extension W_{1+\infty} of the Lie algebra of differential operators on the circle consisting of operators of order \geq n. We classify the unitary quasifinite highest weight modules over W_{\infty}=W_{\infty}^{1} and realize them in terms of unitary highest weight representations of the Lie algebra of infinite matrices with finitely many non-zero diagonals.

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