Finite W-algebras

Abstract

Finite versions of W-algebras are introduced by considering (symplectic) reductions of finite dimensional simple Lie algebras. In particular a finite analogue of $W_3^{(2)}$ is introduced and studied in detail. Its unitary and non-unitary, reducible and irreducible highest weight representations are constructed.

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Cited by in corpus (15)

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• Newton-Hooke type symmetry of anisotropic oscillators
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• Classifying relaxed highest-weight modules for admissible-level Bershadsky-Polyakov algebras
• Finite W Algebras and Intermediate Statistics
• The Kazhdan-Lusztig conjecture for finite W-algebras
• Polynomial algebras of superintegrable systems separating in Cartesian coordinates from higher order ladder operators
• Geometry of W-algebras from the affine Lie algebra point of view
• On the Lagrangian Realization of Non-Critical $\mathcal{W}$-Strings
• Supersymmetric structure of the induced W gravities
• On the construction of polynomial Poisson algebras: a novel grading approach