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arXiv · 1112.6347

Alternating subgroups of Coxeter groups and their spinor extensions

O. V. Ogievetsky·L. Poulain d'Andecy
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Abstract

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.

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O. V. Ogievetsky, L. Poulain d'Andecy. 2011-12-29. Alternating subgroups of Coxeter groups and their spinor extensions. https://arxiv.org/abs/1112.6347

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