Super Weyl Groups and Super Coxeter Numbers for Basic Classical Lie Superalgebras — E8 Intelligence Research

FINDING: Super Weyl groups for basic classical Lie superalgebras admit defining sequences and Coxeter graphs, extending Coxeter theory to osp(m|2n) with parity constraints; the super Coxeter number emerges from these defining sequences. | MATH: For osp(m|2n), the super Coxeter number h* = m + 2n − 2 (for m ≥ 2, n ≥ 1, with parity constraints: m even for osp-type B/D, m odd for C-type). Defining sequences encode parity via signed permutations; Coxeter graph nodes carry parity labels (even/odd), and the super Weyl group is a quotient of the affine Weyl group by a parity-twisted relation. Key constants: h* = m + 2n − 2; for osp(1|2n), h* = 2n − 1 (odd, matching the odd root system). | CONNECTION: The super Coxeter number h* = m + 2n − 2 reduces to classical h = 2N − 2 for osp(2N) (m=2N, n=0) — the classical Coxeter number of D_N. For osp(2|2n), h* = 2n, which is the Coxeter number of C_n — a direct lattice/root-system embedding. The parity constraints (even/odd nodes) mirror the Z_2-gradi Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com