Highest weight vector
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Let V be a representation of a Lie algebra 
, resp. a Lie group G. A weight vector 
of weight λ is called a highest weight vector, or vector of highest weight, if all other weights of V are smaller (see ordering of weights) than λ.
Usually, it is assumed that a highest weight vector is a highest weight of a highest weight module (i.e. the representation is generated by v).
