O. V. Ogievetsky, L. Poulain d`Andecy. Alternating subgroups of Coxeter groups and their spinor extensions
Natural Sciences / Mathematics / Algebra
Submitted on: Sep 12, 2012, 17:37:23
Description: Let $G$ be a discrete Coxeter group, $G^+$ its alternating subgroup and $tilde{G}^+$ the spinor cover of $G^+$. A presentation of the groups $G^+$ and $tilde{G}^+$ is proved for an arbitrary Coxeter system $(G,S)$; the generators are related to edges of the Coxeter graph. Results of the Coxeter--Todd algorithm - with this presentation - for the chains of alternating groups of types A, B and D are given.