Quasifinite Highest Weight Modules over Super $W_{1+\infty }$ Algebra

Abstract

We study quasifinite highest weight modules over the supersymmetric extension of the $W_{1+\infty }$ algebra on the basis of the analysis by Kac and Radul. We find that the quasifiniteness of the modules is again characterized by polynomials, and obtain the differential equations for highest weights. The spectral flow, free field realization over the $(B,C)$--system, and the embedding into $\Glinf$ are also presented.

38 pages, Plain Tex, YITP/K-1055, UT-670, SULDP-1994-2

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Cited by in corpus (6)

• Twin-plane-partitions and $\mathcal{N}=2$ affine Yangian
• Plane Partition Realization of (Web of) W-algebra Minimal Models
• Quasifinite representations of the Lie superalgebra of quantum pseudo differential operators
• Etingof Trace, Path Hypergeometric Functions and Integrable Systems
• Representations of Centrally-Extended Lie Algebras over Differential Operators and Vertex Algebras
• Lie subalgebras of differential operators on the super circle