Quasifinite representations of W_{\infty}
Abstract
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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- October 1999
- DOI:
- 10.48550/arXiv.math/9910172
- arXiv:
- arXiv:math/9910172
- Bibcode:
- 1999math.....10172K
- Keywords:
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- Quantum Algebra;
- Representation Theory
- E-Print:
- Amstex, 18 pages