While Large Language Models (LLMs) demonstrate increasingly sophisticated affective capabilities, the internal mechanisms by which they process complex emotions remain unclear. Existing interpretability approaches often treat models as black boxes or focus on coarse-grained basic emotions, leaving the cognitive structure of more complex affective states underexplored. To bridge this gap, we propose a Cognitive Reverse-Engineering framework based on Representation Engineering (RepE) to analyze social-comparison jealousy. By combining appraisal theory with subspace orthogonalization, regression-based weighting, and bidirectional causal steering, we isolate and quantify two psychological antecedents of jealousy, Superiority of Comparison Person and Domain Self-Definitional Relevance, and examine their causal effects on model judgments. Experiments on eight LLMs from the Llama, Qwen, and Gemma families suggest that models natively encode jealousy as a structured linear combination of these constituent factors. Their internal representations are broadly consistent with the human psychological construct, treating Superiority as the foundational trigger and Relevance as the ultimate intensity multiplier. Our framework also demonstrates that toxic emotional states can be mechanically detected and surgically suppressed, suggesting a possible route toward representational monitoring and intervention for AI safety in multi-agent environments.