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Highest Weight Representation And Lowest Weight RepresentationIn representation theory, the space of all possible weights is a vector space. Let's fix a total ordering of this vector space such that a nonnegative linear combination of positive vectors with at least one nonzero coefficient is another positive vector. Then, a representation is said to have highest weight λ if λ is a weight and all its other weights are less than λ. Similarly, it is said to have lowest weight λ if λ is a weight and all its other weights are greater than it.
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