Quasifinite representations of classical Lie subalgebras of W_{1+infty}

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dc.creatorKac, Victor G.
dc.creatorWang, Weiqiang
dc.creatorYan, Catherine H.
dc.date1998-01-29
dc.date.accessioned2026-07-07T05:23:43Z
dc.date.available2026-07-07T05:23:43Z
dc.descriptionWe show that there are precisely two, up to conjugation, anti-involutions sigma_{\pm} of the algebra of differential operators on the circle preserving the principal gradation. We classify the irreducible quasifinite highest weight representations of the central extension \hat{D}^{\pm} of the Lie subalgebra of this algebra fixed by - sigma_{\pm}, and find the unitary ones. We realize them in terms of highest weight representations of the central extension of the Lie algebra of infinite matrices with finitely many non-zero diagonals over the truncated polynomial algebra C[u] / (u^{m+1}) and its classical Lie subalgebras of B, C and D types. Character formulas for positive primitive representations of \hat{D}^{\pm} (including all the unitary ones) are obtained. We also realize a class of primitive representations of \hat{D}^{\pm} in terms of free fields and establish a number of duality results between these primitive representations and finite-dimensional irreducible representations of finite-dimensional Lie groups and supergroups. We show that the vacuum module V_c of \hat{D}^+ carries a vertex algebra structure and establish a relationship between V_c for half-integral central charge c and W-algebras.
dc.descriptionLatex, 77 pages
dc.identifierhttps://arxiv.org/abs/math/9801136
dc.identifierhttp://arxiv.org/abs/math/9801136
dc.identifierAdv. in Math. 39 (1998) 56--140
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76549
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subjectRepresentation Theory
dc.titleQuasifinite representations of classical Lie subalgebras of W_{1+infty}
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