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Zbl 0974.17033
Kac, Victor G.; Liberati, José I.
Unitary quasi-finite representations of $W_\infty$. (English)
[J] Lett. Math. Phys. 53, No.1, 11-27 (2000). ISSN 0377-9017; ISSN 1573-0530/e

{\it H. Awata, M. Fukuma, Y. Matsuo} and {\it S. Odake} [J. Phys. A 28, 105-112 (1995; Zbl 0852.17025)] developed a theory of quasi-finite highest-weight representations of the subalgebras $W_{\infty, p}$ ($p\in\Bbb C[x]$) of $W_{1+\infty}$, the most important being $W_{\infty}=W_{\infty, x}$. In the paper under review the authors develop a general approach to these problems by following the basic ideas in [{\it V. Kac} and {\it A. Radul}, Commun. Math. Phys. 157, 429-457 (1993; Zbl 0826.17026)]. The main result is the classification and construction of all unitary irreducible quasi-finite highest-weight modules over $W_{\infty}$. These modules are realized in terms of unitary highest-weight representations of the Lie algebra of infinite matrices with finitely many nonzero diagonals.
[M.Primc (Zagreb)]

MSC 2000:: *17B68 Virasoro and related algebras
81R10 Repres. of infinite-dim. groups and algebras from quantum theory
17B70 Graded Lie algebras

Keywords: quasi-finite highest-weight modules

Citations: Zbl 0852.17025; Zbl 0826.17026

Cited in: Zbl 1153.81327

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