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Showing 1 to 12 of 12 for “"Coxeter groups"”.
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Efficient algorithms in Coxeter groups of large type
… time algorithm for the conjugacy problem for Coxeter groups of large type. We also give conditions on the relators of a large-type Coxeter group that are necessary and sufficient for the group to be hyperbolic, and we give a normal form for large-type Coxeter groups that is a regular …
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Antilinear deformations of Coxeter groups with application to Hamiltonian systems
… which is extended to factorizations of the Coxeter element and a reduced Coxeter element thereafter. An antilinear deformation method for the longest element of the Weyl group is given as well. Our last construction method leads to an alternative construction for q-deformed roots. For each …
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The Schurian association schemes associated with parabolic subgroups of Coxeter groups
… all cases where double coset algebras of string Coxeter groups with respect to maximal parabolic subgroups have the involutive double coset property. For infinite affine string Coxeter groups, this property was only known to occur in the case of the vertex stabilizer for the types ˜C2 and ˜G 2, …
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On the symmetric generation of finite groups
… In Chapter 3 our attention turns to Coxeter groups. We show how the Coxeter-Moser presentations traditionally associated with the families of finite Coxeter groups of types A\(_n\), D\(_n\) and E\(_n\) (ie the “simply laced” Coxeter groups) may be interpreted as symmetric …
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The combinatorics of reduced decompositions
… aspects of reduced decompositions in finite Coxeter groups. Effort is primarily concentrated on the symmetric group, although some discussions are subsequently expanded to finite Coxeter groups of types B and D. In the symmetric group, the combined frameworks of permutation patterns and …
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Embeddings of cat(0) cube complexes in products of trees
In ‘Groups acting on connected cubes and Kazhdan’s property T’, [29], Niblo and Roller showed that any CAT(0) cube complex embeds combinatorially and quasi-isometrically in the Hilbert space '2(H) where H is the set of hyperplanes. This Hilbert space may be viewed as the completion of an infinite …
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Separability within alternating groups and randomness
… promotes known residual properties of free groups, surface groups, right angled Coxeter groups and right angled Artin groups to the situation where the quotient is only allowed to be an alternating group. The proofs follow two related threads of ideas. The first thread leads to `alternating' …
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New computational methods for analysing finitely-presented groups
… methods for the analysis of finitely-presented groups and show their usefulness in a variety of contexts. The first procedure creates a labelled coset graph which can be used for rewriting and also for finding expressions for subgroup elements in terms of given generators. We use this procedure …
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On complex reflection groups G(m, 1, r) and their Hecke algebras
… elements in a G(m, 1, r). A Bruhat order on the groups is also defined and investigated. We generalize the Geck-Pfeiffer reducibility theorem for finite Coxeter groups to the groups G(m, 1, r). Based on this, we prove that a character value of any element in an Ariki-Koike algebra (the Hecke …
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Studies on quasisymmetric functions
… Ceballos and Labbé on reduced-word graphs in Coxeter groups (joint work with Alexander Postnikov). Given an element of a Coxeter group, we can form a graph whose vertices are the reduced expressions of this element, and whose edges connect two reduced expressions which are "a single braid move …
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Permutation Patterns, Reduced Decompositions with Few Repetitions and the Bruhat Order
<p>This thesis is concerned with problems involving permutations. The main focus is on connections between permutation patterns and reduced decompositions with few repetitions. Connections between permutation patterns and reduced decompositions were first studied various mathematicians including …