Fusion algebra at a rational level and cohomology of nilpotent subalgebras of sl_2

Abstract

We define and calculate the fusion algebra of WZW model at a rational level by cohomological methods. As a byproduct we obtain a cohomological characterization of admissible representations of $\widehat{\gtsl}_{2}$.

11 pages

Cited by in corpus (22)

• An algebraic approach to logarithmic conformal field theory
• Logarithmic Conformal Field Theory: Beyond an Introduction
• Fusion rules and logarithmic representations of a WZW model at fractional level
• Modular Data and Verlinde Formulae for Fractional Level WZW Models I
• The su(2)_{-1/2} WZW model and the beta-gamma system
• Comments on nonunitary conformal field theories
• sl^(2)_{-1/2}: A Case Study
• sl(2)_{-1/2} and the Triplet Model
• Fusion, Crossing and Monodromy in Conformal Field Theory Based on $SL(2)$ Current Algebra with Fractional Level
• Conformal Blocks for admissible representations in SL(2) current algebra
• $A_1^{(1)}$ Admissible Representations -- Fusion Transformations and Local Correlators
• An admissible level $\widehat{\mathfrak{osp}}\left(1|2\right)$-model: modular transformations and the Verlinde formula
• Operator product expansion in SL(2) conformal field theory
• Fusion rules and singular vectors of the osp(1|2) current algebra
• Notes on the Verlinde formula in non-rational conformal field theories
• A note on decoupling conditions for generic level $\widehat{sl}(3{)}_k$ and fusion rules
• Free field realization of SL(2) correlators for admissible representations, and hamiltonian reduction for correlators
• On Principal Admissible Representations and Conformal Field Theory
• Fusion rules for admissible representations of affine algebras: the case of $A_2^{(1)}$
• Notes on SL(2) conformal fields theories. Exact solution and applications
• Highest-weight vectors and three-point functions in GKO coset decomposition
• Characters of $\widehat{sl}(4{)}_k$ fusion algebra at non-rational level