coxeter group
How many elements of a Coxeter group have a unique reduced expression?
... a Coxeter group W with distinguished generating set R, every element w of W may be written as a word in ...the Coxeter graph of W the number of elements that have a unique reduced ...
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How many elements of a Coxeter group have a unique reduced expression?
... a Coxeter group W with distinguished generating set R, every element w of W may be written as a word in ...the Coxeter graph of an arbitrary Coxeter group W the number of elements that ...
8
The Coxeter group Dn
... We make two observations about these growth polynomials. First, each growth series is a product of cyclotomic polynomials. Second, the value of the series at 1 is the order of the corresponding group and the ...
6
A Clifford Algebraic Framework for Coxeter Group Theoretic Computations
... conformal group C(1, 3) is ...Sitter group, corresponding to the homogeneous space- time that is the solution of Einstein’s field equations with a negative cosmological constant, Λ < ...0) group ...
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A Clifford Algebraic Framework for Coxeter Group Theoretic Computations
... conformal group C(p, q) is 1 − 2-homomorphic to O(p + 1, q + 1) [1, 2], for which one can easily construct the Clifford algebra and find rotor implementations of the conformal group action, including ...
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Involution products in Coxeter groups
... and 0 0 l A Z, and set w ¼ gðl; l; 2lÞ. Clearly g and ðl; l; 2lÞ commute and ðl; l; 2lÞ has infinite order. Therefore w has infinite order. If w can be written as a product of two involutions, then there exist hm; kn A W ...
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Antilinear deformations of Coxeter groups, an application to Calogero models
... One deficiency of the above constructions is that in some cases they do not lead to any complex solution for ˜ ∆. However, we demonstrate now that in these cases one may still construct higher dimensional solutions by ...
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Clifford Algebra Unveils a Surprising Geometric Significance of Quaternionic Root Systems of Coxeter Groups
... current group theoretic paradigm for reflection groups is Coxeter group theory [4, 17], which axiomatises reflections from an abstract mathematical point of ...in Coxeter theory thus ...the ...
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Generalizations of Artin and Coxeter monoids
... the group may be represented by positive words on ...a Coxeter group may be considered as a monoid with the same ...a Coxeter group. Lemma 1.5.21. A Coxeter group W has a ...
175
The descent algebras of Coxeter groups
... tlie Coxeter groups of type I, or dihedral groups was realised, as was a basis of minimal idempotents for tlie descent algebra of any Coxeter group, lifted from the parabolic Burnside ring into the ...
114
On excess in finite Coxeter groups
... 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 ...
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Exactly solvable potentials of Calogero type for q-deformed Coxeter groups
... Our manuscript is organized as follows: In the next section we recall the notion of solvability based on the fact that certain types of Hamiltonians can be formulated in terms of the generators of the Borel subalgebra of ...
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X posets of certain Coxeter groups
... Abstract. Let X be a subgroup of a Coxeter group W . In [5], the authors developed the notion of X-posets, which are defined on certain equivalence classes of the (right) cosets of X in W . These posets can ...
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Novel Kac-Moody-type affine extensions of non-crystallographic Coxeter groups
... In conclusion, we note that all results in Ref. [21] and Ref. [8] have been rationalised here in a Coxeter group framework. For affine reflections perpendicular to 2-fold axes, the corresponding ...
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Partial normalizations of coxeter arrangements and discriminants
... Abstract. We study natural partial normalization spaces of Coxeter arrangements and discriminants and relate their geometry to representation theory. The underlying ring structures arise from Dubrovin’s Frobenius ...
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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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A (very short) introduction to buildings
... algebraic group defined over ...Weyl group of G, where N is the normalizer in G of T ...finite Coxeter group (W, S ) with S = {s i } i∈I ...
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Automorphisms of Right Angled Coxeter Groups
... The properties of a right-angled Coxeter group W depend almost exclusively on the combinatorics of the diagram Γ. This is especially evident in the study of AutW. For example, the groupoid FΓ consisting of ...
10
The decomposition into cells of the affine Weyl groups of type A
... In [1], Kazhdan and Lusztig introduce the concept of a W-graph for a Coxeter group W. In particular, they define left, right and two-sided cells. These W-graphs play an important role in the representation ...
244
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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