A subrepresentation is an invariant subspace of a group representation or Lie algebra representation, with the restricted action.
For a subrepresentation , the quotient vector space inherits the action. For a Lie algebra representation, the formula is , well-defined because is invariant.
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Subrepresentation typically refers to a scenario in which a particular group, category, or demographic is underrepresented in a given context or setting. This concept often comes up in discussions related to diversity and inclusion, especially in fields like politics, education, media, and the workplace. For example, if women hold only a small percentage of leadership positions within a company, that would exemplify subrepresentation of women in leadership.