Quantum reduction and representation theory of superconformal algebras

By V. Kac, M. Wakimoto. 2003

260 citations recorded by the source corpus.

Abstract We study the structure and representations of a family of vertex algebras obtained from affine superalgebras by quantum reduction. As an application, we obtain in a unified way free field realizations and determinant formulas for all superconformal algebras.

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

View Paper: https://www.semanticscholar.org/paper/23ae8c23b6df4b5e021eb5dfdc9d9cfadec7628e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. T. Arakawa
2. A. Sole
3. A. Premet
4. V. Kac
5. I. Losev
6. J. Duncan
7. Miranda C. N. Cheng
8. Yuji Tachikawa

In Geometry and Topology

1. T. Arakawa
2. A. Sole
3. A. Premet
4. J. Duncan
5. Miranda C. N. Cheng
6. V. Kac
7. Tohru Eguchi
8. J. Harvey

In Statistical and Nonlinear Physics

1. A. Premet
2. A. Sole
3. T. Arakawa
4. Tohru Eguchi
5. J. Duncan
6. Yuji Tachikawa
7. J. Harvey
8. Hirosi Ooguri

Citations in the corpus

• Umbral Moonshine (2012, background): “[16, 17, 18]) that this algebra contains subalgebras isomorphic to the affine Lie algebra ŝl2 and the Virasoro algebra, and in a unitary representation the former of these acts with level m− 1, for some integer m > 1, and the latter with central charge c = 6(m− 1), and the unitary irreducible highes”
• Enveloping algebras of Slodowy slices and the Joseph ideal (2005, methodology): “It should be mentioned here that V.G. Kac and M. Wakimoto described minimal nilpotent superconformal algebras in the context of vertex operators and quantum reduction; see [22] and the references therein.”
• Finite vs affine W-algebras (2005, methodology): “This and the parallel, simpler notion of a non-linear Lie algebra, are discussed in Section 3. It follows from [DK, KW1 ] that all affineW-algebras can be obtained as universal enveloping vertex algebras of certain non-linear Lie conformal algebras.”
• The Gelfand-Kirillov conjecture and Gelfand-Tsetlin modules for finite W-algebras (2010, unknown): “All rights reserved. doi:10.1016/j.aim.2009.08.018 the works of Feigin and Frenkel [13], Kac et al. [25], Kac and Wakimoto [24] and De Sole and Kac [36].”
• Quantum Reduction for Affine Superalgebras (2003, unknown): “ormal algebra. Note that it was already established by Khovanova [Kh] that the classical reduction of sℓ(2|1)b produces the N = 2 superconformal algebra. Further examples and results are presented in [KW5], where, in particular, we give a proof of a stronger form of the fundamental Conjecture 2.1 of”
• Representation theory of W-algebras (2005, background): “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.”
• Notes on the K3 Surface and the Mathieu Group M 24 (2010, background): “For a rigorous mathematical exposition, see, for example, [Kac 98, Kac and Wakimoto 04].”