Ladder operator

A ladder operator maps weight vectors to weight vectors whose weights differ by one root. Positive-root vectors raise weights and negative-root vectors lower them.

A raising operator is a positive-root vector. Acting on a weight vector of weight $\mu$ either gives zero or a weight vector of weight $\mu +\alpha$.

A lowering operator is a negative-root vector. Acting on a weight vector of weight $\mu$ either gives zero or a weight vector of weight $\mu -\alpha$.