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Letwhereis a field withbe the space of structure vectors of algebras having the  n -dimensional-space  V  as the underlying vector space. Also letRegardingas a  G -module via the ‘change of basis’ action of  G  on  V , we determine the composition factors of various  G -submodules ofwhich correspond to certain important families of algebras. This is achieved by introducing the notion of linear degeneration which allows us to obtain analogues overof certain known results on degenerations of algebras. As a result, the  GL ( V )-structure ofis determined.

Linear degenerations of algebras and certain representations of the general linear group