On simplicity of vacuum modules
arXiv:math-ph/0606002
Abstract
We find necessary and sufficient conditions of irreducibility of vacuum modules over affine Lie algebras and superalgebras. From this we derive conditions of simplicity of minimal W-algebras. Moreover, in the case of Virasoro and Neveu-Schwarz algebras we obtain explicit formulas for vacuum determinants.
54 pages. 6/14/06: Corollary 9.1.5(ii) is replaced by a complete version and its proofis added