Quantum Reduction for Affine Superalgebras

By V. Kac, Shi-Shyr Roan, M. Wakimoto. 2003

300 citations recorded by the source corpus.

We extend the homological method of quantization of generalized Drinfeld–Sokolov reductions to affine superalgebras. This leads, in particular, to a unified representation theory of superconformal algebras.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/27c53e91022fac6a81e4eb164c087d4666378e5f

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Citations in the corpus

Shifted Yangians and finite W-algebras (2004, background): “is injective for j ≤ −1, surjective for j ≥ −1. This definition originates in [ KRW ] in the study of certain W-algebras defined from affine Lie algebras by quantum Hamiltonian reduction.”
Representation theory of W-algebras (2005, unknown): “In view of [14, 36, 40], the W -algebras Wk(ḡ) considered in this article are the W -algebras associated with principal nilpotent orbits of ḡ.”
The Gelfand-Kirillov conjecture and Gelfand-Tsetlin modules for finite W-algebras (2010, unknown): “[25], Kac and Wakimoto [24] and De Sole and Kac [36].”
Representations of Shifted Yangians and Finite W-algebras (2005, methodology): “This is a good grading for e ∈ g1 in the sense of [ KRW ] (see also [EK] for the full classification).”
Plane partitions with a “pit”: generating functions and representation theory (2015, methodology): “Note that our W -algebras differ from the ones introduced in [27].”
Vertex algebras at the corner (2017, methodology): “The quantum DS reduction for WZW VOA’s based on super-Lie algebras works in the same way as for standard Lie algebras, except that fermionic ghosts are replaced by bosonic ghosts in the odd components of n [38].”
Finite vs affine W-algebras (2005, methodology): “Though, for simplicity, we assumed above that g is a Lie algebra, we work in the more general situation of a simple finite-dimensional Lie superalgebra g with a non-degenerate supersymmetric invariant bilinear form, as in [ KRW , KW1, KW2].”
Conformal embeddings of affine vertex algebras in minimal W-algebras I: Structural results (2016, methodology): “In [21], [24] a vertex algebra W k(g, f), called a universal W-algebra, has been associated to each triple (g, f, k), where g is a basic simple Lie superalgebra with a non-degenerate invariant supersymmetric bilinear form, f is a nilpotent element of g0̄, and k ∈ C, by applying the quantum Hamiltoni”