Fleischmann, P. (2002) On pointwise conjugacy of distinguished coset representatives in Coxeter groups. Journal of Group Theory, 5 (3). pp. 269-283. ISSN 1433-5883.
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Let (W, S) be a Coxeter system. For a standard parabolic. subgroup W-K, K subset of or equal to S let D-K be the set of distinguished coset representatives, i.e. representatives of cosets W(K)w of minimal Coxeter length. If L = K-c subset of or equal to S with c is an element of W, then D-K and D-L = c(-1) D-K are in general not conjugate as sets. However it is shown that if WK is finite, they are conjugate 'pointwise', i.e. there is a bijection theta : D-K --> D-L such that theta(d) = d(wc) for some w is an element of W-K depending on d is an element of D-K. In particular for each conjugacy class C of W the cardinalities # (D-K boolean AND C) and # (D-L boolean AND C) are the same. The case of infinite standard parabolic subgroups is also discussed and a corresponding result is proved.
|Subjects:||Q Science > QA Mathematics (inc Computing science)|
|Divisions:||Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science|
|Depositing User:||Judith Broom|
|Date Deposited:||19 Dec 2007 18:18|
|Last Modified:||14 Jan 2010 13:58|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/522 (The current URI for this page, for reference purposes)|
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