Introduction to prehomogeneous vector spaces

By Tatsuo Kimura. 2002

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Representation zeta functions of nilpotent groups and generating functions for Weyl groups of type B (2011, background): “The list of irreducible reduced PVS in the appendix of [25] starts off with three infinite families of prehomogeneous vector spaces of generic matrices, viz.”
Maximally homogeneous para-CR manifolds of semisimple type (2006, unknown): “onℓρ onthe vectorspaceV = Rn. Such a representation will be called linear. A vector space V with a linear G-action, which has an open orbit, is traditionally called a prehomogeneous vector space (see [68]). Quite opposite to a linear representation is the situation that the aﬃne representation ρis t”
Half‐flat structures and special holonomy (2009, background): “This result can be viewed as a consequence of the theory of prehomogeneous vector spaces [31] as follows.”