Coxeter groups
Coxeter Groups as Beauville Groups
... [finite] groups admit Beauville structures?” as well as the more difficult question of which Beauville groups are strongly real Beauville ...finite groups including abelian groups [7]; ...
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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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Maximal length elements of excess zero in Finite Coxeter Groups
... 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 groups and the ...
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Maximal length elements of excess zero in finite Coxeter Groups
... irreducible Coxeter group, and hence for all finite Coxeter ...Weyl groups, it appears that every element of maximal length in a conjugacy class has excess ...
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Affine extensions of non-crystallographic Coxeter groups induced by projection
... crystallographic groups by two nodes and show that these do not induce any further affine ...non-crystallographic Coxeter groups from a recent paper and compare the induced extensions with the ...
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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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Quasiparabolic Subgroups of Coxeter Groups and Their Hecke Algebra Module Structures
... Coxeter groups. We manage to solve the problem for all finite classical Coxeter groups, and the quasiparabolic subgroups are listed in Theorem 16 of Chapter ...
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Antilinear deformations of Coxeter groups with application to Hamiltonian systems
... Systems such as Calogero models and Toda field theories can be related to root systems coupled to Coxeter groups or Weyl groups in complete gen- erality [38][39][40]. In single particle systems it is ...
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A note on commuting Involution Graphs in Affine Coxeter Groups
... Weyl groups (see [7], [6] and ...affine groups? The purpose of this short note is to establish some general results for commuting involution graphs in affine Coxeter groups, and to deal with ...
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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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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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Involution Posets of Non-Crystallographic Coxeter Groups
... of Coxeter groups of type H , excluding the identity, is the set of order 2 elements of the group (or involutions of the group) ...the Coxeter groups of type H is ...
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Exactly solvable potentials of Calogero type for q-deformed Coxeter groups
... It has been shown previously that solvability of certain types of Hamiltonians can be es- tablished [17, 18, 19, 20] by relating the differential operators inside the Hamiltonians, that is essentially the Laplace ...
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Clifford Algebra Unveils a Surprising Geometric Significance of Quaternionic Root Systems of Coxeter Groups
... rank-3 Coxeter groups can be represented by the pure quaternion part of the representations of the rank-4 groups they generate as spinors if and only if they contain the central ...
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Novel Kac-Moody-type affine extensions of non-crystallographic Coxeter groups
... Kac-Moody approach in Lie Theory. Under the assumption that the extended matrix is symmetric, a unique affine extension has been obtained in each case. In Ref. [8] it was shown that this approach is not sufficient for ...
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Affine Toda field theories related to Coxeter groups of noncrystallographic type
... Noting that for the Coxeter groups we consider the Cartan matrices are symmetric, such that the relations (2.9) also hold with i ↔ j. As the right hand side involves only one inner product in ˜ ∆, this ...
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A note on maximal length elements in conjugacy classes of finite coxeter groups
... 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 groups and the ...
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Involution statistics in finite coxeter groups
... that Coxeter groups have a very special relationship with ...a Coxeter group (conjugates of fundamental reflections) is in one-to- one correspondence with its set of positive ...a Coxeter ...
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Symmetric Presentations of Coxeter Groups
... We slightly generalize the notion of a ‘graph with a tail’ and, in doing so, provide symmetric presentations for all the simply laced irreducible finite Coxeter groups with the aid of little more than a ...
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The descent algebras of Coxeter groups
... After this initial description in 1976, little more was achieved, until 1984, when Etienne, [Eti84], proved a result from which the existence of the descent algebra of the Coxeter groups of type A, or tlie ...
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