Coxeter covers of the classical coxeter groups

Meirav Amram, Robert Shwartz, Mina Teicher

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Let C(T) be a generalized Coxeter group, which has a natural map onto one of the classical Coxeter groups, either Bn or Dn. Let CY(T) be a natural quotient of C(T), and if C(T) is simply-laced (which means all the relations between the generators has order 2 or 3), C Y(T) is a generalized Coxeter group, too. Let At,n be a group which contains t Abelian groups generated by n elements. The main result in this paper is that CY(T) is isomorphic to At,n ⋊ Bn or At,n ⋊ Dn, depends on whether the signed graph T contains loops or not, or in other words C(T) is simply-laced or not, and t is the number of the cycles in T. This result extends the results of Rowen, Teicher and Vishne to generalized Coxeter groups which have a natural map onto one of the classical Coxeter groups.

Original languageEnglish
Pages (from-to)1041-1062
Number of pages22
JournalInternational Journal of Algebra and Computation
Volume20
Issue number8
DOIs
StatePublished - Dec 2010

Bibliographical note

Funding Information:
The first author was partially supported by the Emmy Noether Research Institute for Mathematics (center of the Minerva Foundation of Germany), the Excellency Center “Group Theoretic Methods in the Study of Algebraic Varieties” of the Israel Science Foundation, and EAGER (EU network, HPRN-CT-2009-00099).

Keywords

  • Classical Coxeter groups
  • affine Coxeter groups
  • signed graphs
  • signed permutations

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