WebTheorem D. Let (W,S) be a Coxeter system and let u ∈ W be cyclically reduced. Then the following are equivalent: (1) u is straight. (2) Every cyclically reduced conjugate of u obtained from u by a sequence of braid relations and cyclic shifts is torsion-free. Example 1. Let W be the affine Coxeter group of type A˜2, with set of generators S ... WebON THE CYCLICALLY FULLY COMMUTATIVE ELEMENTS OF COXETER GROUPS TOM BOOTHBY, JEFFREY BURKERT, MORGAN EICHWALD, AND MATTHEW MACAULEY ABSTRACT. Let W be a Coxeter group. We say that w ∈ W is cyclically fully commutative (CFC) if every cyclic shift of every reduced expression for w is fully …
Cyclic permutation - Wikipedia
WebDec 6, 2024 · Cyclically reduced elements in Coxeter groups. Let $W$ be a Coxeter group. We provide a precise description of the conjugacy classes in $W$, yielding an analogue … WebCoxeter groups satisfy Theorem A. Recall that an element w∈W is cyclically reduced if ‘ S(w0) = ‘ S(w) for every w0∈W obtained from wby a sequence of cyclic shifts. Often, this terminology is used instead for elements of minimal length in their conjugacy class. An … how old is german player muller
Cyclically reduced elements in Coxeter groups - Semantic …
WebThese generalize Coxeter elements in that their reduced expressions can be described combinatorially by acyclic directed graphs, and cyclically shifting corresponds to … Webthe straight elements in the class of so-called cyclically fully commutative (CFC) elements (which \generalises" in some sense the class of Coxeter elements), provided that Wsatis es some additional technical condition. An obvious requirement for an arbitrary element w2W to be straight is that it should be cyclically reduced (see e.g. Lemma 4.1 ... Webrepresentatives in right-angled Artin and Coxeter groups. We prove regularity of the conjugacy geodesic language for virtual graph products in certain cases, and highlight ... two cyclically reduced elements in a RAAG are conjugate if and only if they are related by a finite sequence of cyclic permutations and commutation relations [15]. We ... mercs used