A weight lattice is a geometric structure that represents the weights of a representation of a Lie algebra or Lie group. It is formed by the integral linear combinations of the fundamental weights, which correspond to the vertices of a lattice in a Euclidean space. This concept is crucial for understanding the representation theory of semisimple Lie algebras and plays a significant role in various applications, including the Borel-Weil theorem, where it connects geometric objects to algebraic structures.
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