The aim of this paper is to study relations between regular reductive PVs with one-dimensional scalar multiplication and the structure of graded Lie algebras. We will show that the regularity of such PVs is described by an $\mathfrak{sl}_2$-triplet of a graded Lie algebra.
Study of parity sheaves arising from graded Lie algebra
Semisimple elements and the little Weyl group of real semisimple $Z_m$-graded Lie algebras
Cohomology and deformations of the infinite dimensional filiform Lie algebra m_2
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