Irreducibility refers to a property of representations where a representation cannot be decomposed into smaller, non-trivial representations. This concept is essential in understanding how representations function within the framework of group theory and helps to establish the structure of representations through induction and restrictions. Recognizing whether a representation is irreducible has significant implications for the analysis of induced representations and their properties, as well as for understanding the Frobenius reciprocity theorem.
congrats on reading the definition of irreducibility. now let's actually learn it.