Centers and Coxeter Elements
نویسندگان
چکیده
Suppose that G is a connected compact Lie group. We show that simple numerical information about the Weyl group of G can be used to obtain bounds, often sharp, on the size of the center of G. These bounds are obtained with the help of certain Coxeter elements in the Weyl group. Variants of the method use generalized Coxeter elements and apply to p-compact groups; in this case a splitting theorem emerges. The Lie group results are mostly known, but our arguments have a conceptual appeal.
منابع مشابه
Clusters, Coxeter-sortable Elements and Noncrossing Partitions
We introduce Coxeter-sortable elements of a Coxeter group W. For finite W, we give bijective proofs that Coxeter-sortable elements are equinumerous with clusters and with noncrossing partitions. We characterize Coxeter-sortable elements in terms of their inversion sets and, in the classical cases, in terms of permutations.
متن کاملOn the Maximally Clustered Elements of Coxeter Groups
We continue the study of the maximally clustered elements for simply laced Coxeter groups which were recently introduced by Losonczy. Such elements include as a special case the freely braided elements of Losonczy and the author, which in turn constitute a superset of the iji-avoiding elements of Fan. Our main result is to classify the MC-finite Coxeter groups, namely those Coxeter groups havin...
متن کاملEssays on Coxeter groups Coxeter elements in finite Coxeter groups
A finite Coxeter group possesses a distinguished conjugacy class of Coxeter elements. The literature about these is very large, but it seems to me that there is still room for a better motivated account than what exists. The standard references on thismaterial are [Bourbaki:1968] and [Humphreys:1990], butmy treatment follows [Steinberg:1959] and [Steinberg:1985], from which the clever parts of ...
متن کاملConjugacy of Coxeter Elements
For a Coxeter group (W,S), a permutation of the set S is called a Coxeter word and the group element represented by the product is called a Coxeter element. Moving the first letter to the end of the word is called a rotation and two Coxeter elements are rotation equivalent if their words can be transformed into each other through a sequence of rotations and legal commutations. We prove that Cox...
متن کاملCLASSIFICATION OF COXETER GROUPS WITH FINITELY MANY ELEMENTS OF a-VALUE 2
We consider Lusztig’s a-function on Coxeter groups (in the equal parameter case) and classify all Coxeter groups with finitely many elements of a-value 2 in terms of Coxeter diagrams.
متن کامل