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THE ABSOLUTE ORDER OF A PERMUTATION REPRESENTATION OF A COXETER GROUP
 

Summary: THE ABSOLUTE ORDER OF A PERMUTATION
REPRESENTATION OF A COXETER GROUP
CHRISTOS A. ATHANASIADIS AND YUVAL ROICHMAN
Abstract. A permutation representation of a Coxeter group W naturally
defines an absolute order. This family of partial orders (which includes the
absolute order on W ) is introduced and studied in this paper. Conditions
under which the associated rank generating polynomial divides the rank
generating polynomial of the absolute order on W are investigated when W
is finite. Several examples, including a symmetric group action on perfect
matchings, are discussed. As an application, a well-behaved absolute order
on the alternating subgroup of W is defined.
Contents
1. Introduction 1
2. Basic concepts 2
3. Modular subgroups 5
4. Quasi-modular subgroups 13
4.1. Quasi-modularity 13
4.2. Balanced complex reflections 14
4.3. Perfect matchings 15
5. An application to alternating subgroups 18

  

Source: Athanasiadis, Christos - Department of Mathematics, University of Athens

 

Collections: Mathematics