| Softcover ISBN: | 978-2-37905-201-9 |
| Product Code: | AST/457 |
| List Price: | $69.00 |
| AMS Member Price: | $55.20 |
| Softcover ISBN: | 978-2-37905-201-9 |
| Product Code: | AST/457 |
| List Price: | $69.00 |
| AMS Member Price: | $55.20 |
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Book DetailsAstérisqueVolume: 457; 2025; 135 ppMSC: Primary 20
This book gives a definitive solution to the problem of describing conjugacy classes in arbitrary Coxeter groups in terms of cyclic shifts.
Given a Coxeter system \((W, S)\), a cyclic shift of an element \(w\) of \(W\) is a conjugate of \(w\) by a simple reflection whose length is at most the length of \(w\). For a spherical subset \(K\) of \(S\) the author also calls two elements of \(W K\)-conjugate if they normalise the standard parabolic subgroup of type \(K\) and are conjugate to one another by its longest element.
In this paper, the author shows that any two conjugate elements of \(W\) differ only by a sequence of cyclic shifts and \(K\)-conjugations and explains how this sequence can be computed explicitly. Along the way, the author obtains several results of independent interest, such as a description of the centraliser of an infinite order element \(w\) of \(w\), as well as the existence of natural decompositions of \(w\) as a product of a “torsion part” and of a “straight part” with useful properties.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
ReadershipGraduate students and research mathematicians.
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This book gives a definitive solution to the problem of describing conjugacy classes in arbitrary Coxeter groups in terms of cyclic shifts.
Given a Coxeter system \((W, S)\), a cyclic shift of an element \(w\) of \(W\) is a conjugate of \(w\) by a simple reflection whose length is at most the length of \(w\). For a spherical subset \(K\) of \(S\) the author also calls two elements of \(W K\)-conjugate if they normalise the standard parabolic subgroup of type \(K\) and are conjugate to one another by its longest element.
In this paper, the author shows that any two conjugate elements of \(W\) differ only by a sequence of cyclic shifts and \(K\)-conjugations and explains how this sequence can be computed explicitly. Along the way, the author obtains several results of independent interest, such as a description of the centraliser of an infinite order element \(w\) of \(w\), as well as the existence of natural decompositions of \(w\) as a product of a “torsion part” and of a “straight part” with useful properties.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Graduate students and research mathematicians.
