Concealedness and Weyl Groups

摘要: The goal of this chapter is twofold. On one hand we analyze integral quadratic forms \(q:\mathbb {Z}^n \to \mathbb {Z}\) such that there a basis in \(\mathbb {Z}^n\) which q unitary (that is, all diagonal coefficients are equal to one). Such called concealed. Some methods identify concealed discussed, for instance, the positive case make use spectral properties graphs. other study certain subgroups group isometries associated forms, so Weyl groups. Spectral Coxeter transformations presented, as well some relations cyclotomic polynomials with Dynkin and extended diagrams. Further matrices considered, including periodicity phenomena their iterations. Boldt’s construct reviewed, A’Campo’s Howlett’s Theorems.