Structure of conjugacy classes in Coxeter groups/ T. Marquis

Includes bibliographies and indexes.

Introduction -- Priliminaries -- Cyclic shift classes -- Elements of finite order -- The structural conjugation graph -- Combinatorial minimal displacement sets -- Proof of theorem B -- The P-splitting of an element -- Indefinite coxeter groups -- Affine coxeter group.

This paper gives a definitive solution to the problem of describing conjugacy classes in arbitrary Coxeter groups in terms of cyclic shifts. In this paper, we compute explicitely the structural conjugation graph associated to any (possibly twisted) conjugacy class in W, and show in particular that it is connected (that is, any two conjugate elements of W differ only by a sequence of cyclic shifts and K-conjugations).