In the context of algebraic groups and Lie algebras, a **root datum** is a structured way of encoding certain aspects of the symmetries and properties of these mathematical objects. Specifically, a root datum consists of the following components: 1. **A finite set of roots**: These are usually vectors in a Euclidean space, which can be thought of as directions that reflect the symmetries of the system.
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A root datum is a quadruple of dual lattices, roots, and coroots with the natural perfect pairing and reflection axioms. A reductive group with maximal torus has and .