Classification of quasifinite $W_\infty$-modules

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dc.creatorSu, Yucai
dc.creatorXin, Bin
dc.date2005-11-21
dc.date.accessioned2026-07-07T06:51:32Z
dc.date.available2026-07-07T06:51:32Z
dc.descriptionIt is proved that an irreducible quasifinite $W_\infty$-module is a highest or lowest weight module or a module of the intermediate series; a uniformly bounded indecomposable weight $W_\infty$-module is a module of the intermediate series. For a nondegenerate additive subgroup $G$ of $F^n$, where $F$ is a field of characteristic zero, there is a simple Lie or associative algebra $W(G,n)^{(1)}$ spanned by differential operators $uD_1^{m_1}... D_n^{m_n}$ for $u\in F[G]$ (the group algebra), and $m_i\ge0$ with $\sum_{i=1}^n m_i\ge1$, where $D_i$ are degree operators. It is also proved that an indecomposable quasifinite weight $W(G,n)^{(1)}$-module is a module of the intermediate series if $G$ is not isomorphic to $Z$.
dc.descriptionLaTeX, 11 pages. To appear in Israel Journal of Mathematics
dc.identifierhttps://arxiv.org/abs/math/0511523
dc.identifierhttp://arxiv.org/abs/math/0511523
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/105019
dc.subjectRepresentation Theory
dc.subjectQuantum Algebra
dc.subject17B10; 17B65; 17B66; 17B68
dc.titleClassification of quasifinite $W_\infty$-modules
dc.typetext

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