Reduced expressions in semidirect products of Coxeter groups

作者：Edgar Tom^*

来源：Journal of Group Theory, 2010, 13(1): 109-115.

DOI：10.1515/JGT.2009.034

Any normal reflection subgroup (W) over tilde of a Coxeter system (W, S) is a factor in a semi-direct product decomposition of W as described by Bonnafe and Dyer. Namely, S is the union of two subsets I and J such that no element of I is conjugate to an element of J, (W) over tilde is the subgroup generated by W(I)-conjugates of elements of J, and W is the semidirect product of W(I) by (W) over tilde. This note describes the reduced expressions of elements of the form wxw(-1) with w is an element of W(I) and x is an element of W(J) in terms of reduced expressions of x and a suitable element of W(I).

• 出版日期2010-1