Some combinatorial results for complex reflection groups


Can H.

EUROPEAN JOURNAL OF COMBINATORICS, vol.19, no.8, pp.901-909, 1998 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 8
  • Publication Date: 1998
  • Doi Number: 10.1006/eujc.1998.0236
  • Journal Name: EUROPEAN JOURNAL OF COMBINATORICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.901-909
  • Erciyes University Affiliated: Yes

Abstract

In this paper, we prove that a simple system for a subsystem Psi of the complex root system Phi can always be chosen as a subset of the positive system Phi(+) of Phi. Furthermore, we show that a set of distinguished coset representatives can be found for every reflection subgroup of the complex reflection groups. The corresponding results for real crystallographic root systems and their reflection groups (i.e., Weyl groups) are well known (see [9]). (C) 1998 Academic Press.