English

Quasifinite representations of W_{\infty}

Quantum Algebra 2007-05-23 v1 Representation Theory

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.

Keywords

Cite

@article{arxiv.math/9910172,
  title  = {Quasifinite representations of W_{\infty}},
  author = {Victor G. Kac and Jose I. Liberati},
  journal= {arXiv preprint arXiv:math/9910172},
  year   = {2007}
}

Comments

Amstex, 18 pages

R2 v1 2026-07-22T18:04:58.293Z