I am studying the representation theory of some infinite dimensional algebras, for example infinite dimensional Lie-algebras, Kac-Moody algebras, W-algebras. These algebras arise as symmetry algebras of tow-dimensional conformally invariant quantum field theories.
I encountered the case that I have to study representations which are indecomposable, i.e. which cannot be decomposed into a direct sum of irreducible representations. However, in my cases, they always contain a irreducible sub-representation.
How can I name this irreducible sub-representation with a concise, short term so I don't have to write "the irreducible sub-representation of the indecomposable representation" all the time?