We present a new characterization of Cartan isoparametric hypersurfaces in terms of properties of the polynomial that determines the algebraic set of planar normal sections on the homogeneous isoparametric hypersurfaces in spheres. We show that Cartan isoparametric hypersurfaces are the only homogeneous isoparametric hypersurfaces in spheres for which the infinity Laplacian of the polynomial th...

Properties of homogeneous segment sets are investigated in this paper. A universal characterization of homogeneous sets is presented in the form of a polynomial algorithm which decides whether or not a set S is homogeneous with respect to S∗. It is shown that any set of homogeneous segments can be reduced to the uniquely determined minimal base and a polynomial algorithm solving this task is pr...

A relation between Schur algebras and the Steenrod algebra is shown in [Hai10] where to each strict polynomial functor the author naturally associates an unstable module. We show that the restriction of Hai’s functor to a sub-category of strict polynomial functors of a given degree is fully faithful.