Representation Theory of Superconformal Algebras and the Kac-Roan-Wakimoto Conjecture

2004/05/06 by Tomoyuki Arakawa, Arakawa, Tomoyuki · 1 citation
Mathematics · Physics and Astronomy · #17B56 #17B69 #81R10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.math-ph/0405015

openalex publication_date 2004/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the representation theory of the superconformal algebra W_k(g,f_θ) associated with a minimal gradation of g. Here, g is a simple finite-dimensional Lie superalgebra with a non-degenerate, even supersymmetric invariant bilinear form. Thus, W_k(g,f_θ) can be one of the well-known superconformal algebras including the Virasoro algebra, the Bershadsky-Polyakov algebra, the Neveu-Schwarz algebra, the Bershadsky-Knizhnik algebras, the N=2 superconformal algebra, the N=4 superconformal algebra, the N=3 superconformal algebra and the big N=4 superconformal algebra. We prove the conjecture of V. G. Kac, S.-S. Roan and M. Wakimoto for W_k(g,f_θ). In fact, we show that any irreducible highest weight character of W_k(g,f_θ) at any level k∈ C is determined by the corresponding irreducible highest weight character of the Kac-Moody affinization of g.

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