Volodymyr Sobol

Centralizers of nilpotent wedges in real orthogonal Lie algebras so(p,q): a signature-resolved Levi-radical map (Geometry of the vacuum, floor −1)

For a rank-2 nilpotent (a wedge) in a real orthogonal Lie algebra so(p,q), the centralizer decomposes as a reductive part in semidirect product with a nilradical — a framework classical over algebraically closed fields (Springer-Steinberg; Collingwood-McGovern). We give the signa...

An identification of three constructions of one lattice, with the closed transverse trace as its lock (Geometry of the vacuum, floor −1)

A cell of d+1 unit directions with pairwise Gram -1/d arises by a representation-theoretic route (irreducibility of the standard representation of the symmetric group on d+1 letters, then Schur), with no energy, no Hamiltonian and no minimization anywhere in the chain; the single...