We introduce the AI task tensor, a framework for understanding the impact of generative AI on human work. The tensor is based on eight dimensions of tasks performed by a human-AI dyad, organized around the areas of a task's formulation, implementation, and resolution. The dimensions include task definition, AI integration, modality. audit requirement, output definition, decision-making authority, AI type, and human user type. After describing the eight dimensions of the AI task tensor, we provide illustrative projections that show how the tensor might be used to build analytical tractability and management intuition. We demonstrate how the AI task tensor can be used to organize emerging research on generative AI. We propose that the AI task tensor offers a starting point for understanding how work will be performed with the emergence of generative AI.