finite Coxeter groups
Maximal length elements of excess zero in finite Coxeter Groups
... of finite Coxeter groups, and principally those of the irreducible finite Coxeter groups, has come from many directions, for example in the representation theory of these ...
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On excess in finite Coxeter groups
... a finite Coxeter group, then every W -conjugacy class possesses at least one element which simultaneously has minimal length in the conjugacy class and excess equal to ...in finite Coxeter ...
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Involution statistics in finite coxeter groups
... Weyl groups, and describe the relationship between roots and ...Weyl groups, which are then applied in Section 4 to each of types A, B and D in ...exceptional finite Coxeter ...
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A note on maximal length elements in conjugacy classes of finite coxeter groups
... of finite Coxeter groups, and prin- cipally those of the irreducible finite Coxeter groups, has come from many directions, for example in the representation theory of these ...
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Maximal length elements of excess zero in Finite Coxeter Groups
... of finite Coxeter groups, and principally those of the irreducible finite Coxeter groups, has come from many directions, for example in the representation theory of these ...
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Symmetries of Spin Calogero Models
... underlying Coxeter group to identify the correct symmetry algebra of the associated integrable ...particular finite Coxeter groups: B L and G 2 ...
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Affine extensions of non-crystallographic Coxeter groups induced by projection
... crystallographic Coxeter groups. These infinite Coxeter groups are usually constructed directly from the finite Coxeter groups by introducing affine reflection planes ...
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Equivariant K homology for some Coxeter groups
... a Coxeter group and to decide whether the group it is finite (comparing each irreducible component with the finite Coxeter groups of the same ...
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A note on commuting Involution Graphs in Affine Coxeter Groups
... of groups, usually with X being either a conjugacy class or the set of all ...a finite Coxeter group [2], a linear group [3], or a sporadic simple group ...for finite Coxeter ...
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Quasiparabolic Subgroups of Coxeter Groups and Their Hecke Algebra Module Structures
... all finite Coxeter ...all finite classical Coxeter groups, and the quasiparabolic subgroups are listed in Theorem 16 of Chapter ...of finite classical Coxeter ...
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Classes of maximal length reduced words in Coxeter groups
... Commutation Classes of Reduced Words 1.1 Finite Coxeter Groups and Root Systems We begin with a brief overview of basic Coxeter group theory, following [Humphreys].. No originality is cl[r] ...
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Toric Heaps, Cyclic Reducibility, and Conjugacy in Coxeter Groups
... in Coxeter theory, because a cyclic shift of a reduced word is simply a conjugate by an initial or terminal ...in Coxeter theory, which is closely related to ...in Coxeter groups, and we ...
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Antilinear deformations of Coxeter groups with application to Hamiltonian systems
... deforming Coxeter groups in an antilinear ...the Coxeter groups. Deforming the Coxeter groups in such a way will ensure that the deformed groups will remain invariant ...
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Antilinear deformations of Coxeter groups, an application to Calogero models
... generalizations of previously constructed ones in the sense that they are formulated in terms of general roots, that is representation independent and irrespective of a specific Coxeter group. Our derivation of ...
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A Framework for Coxeter Spectral Classification of Finite Posets and Their Mesh Geometries of Roots
... 6.2. Although the Coxeter spectral classification problem for arbitrary finite posets remains unsolved, we have a solution for positive one-peak posets. Indeed, it follows from the results in [17] that for ...
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Bieberbach groups with finite point groups
... Chapter 6 discusses the theory and the calculation of the nonabelian tensor squares of centerless Bieberbach groups with a dihedral point group of order eight. The theory gives us the properties of the ...
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On finite arithmetic groups
... considering groups over Q. For a good introduction to the theory of arithmetic groups see ...to groups defined over Q ...automorphism groups of positive definite quadratic Z -lattices under ...
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Complementation in finite groups
... The most obvious complementation problem to consider is that of groups in which all subgroups have complements; this class was studied" by Hall in H5, and was shown to have a simple stru[r] ...
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On the efficiency of finite groups
... Given two presentations, in general there is no way of deciding whether or not the two presentations define isomorphic groups. However, if we let G be a group with presentations {X | R) and (F | S) we can pass ...
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Exactly solvable potentials of Calogero type for q-deformed Coxeter groups
... transformations. Often one changes the coordinate system by using an explicit represen- tations for the roots in an orthogonal basis, which one may find in various places of the literature, e.g. [29]. Then (5.6) enables ...
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