Braid group
MONODROMY REPRESENTATION OF THE BRAID GROUP
... Kohno and Drinfel’d. Such representations are typically referred to as monodromy representations of the braid group along solutions of the KZ equation. These linear representations are of great interest ...
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Krammer's Representation of the Pure Braid Group, P3
... In Section 2, we introduce some definitions of the pure braid group and Krammer’s representation. In Sections 3 and 4, we present our work that leads to our main theorem, Theorem 4.2, which gives a ...
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ON THE FAITHFULNESS OF JONES-WENZL REPRESENTATION OF THE BRAID GROUP $B_{4}$
... the braid group on n strings, namely the Burau representation, has been shown that it is not faithful for n ≥ 6 ...the braid group have been constructed to attack the question of the ...
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Fock parafermions and self-dual representations of the braid group
... mean the usual quantum field theory notion, which requires a Fock space and thus, second quantization; that is, one needs a way of counting them. That said, by generalizing the concept of particle statistics to localized ...
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On the Irreducibility of Fourth Dimensional Tuba's Representation of the Pure Braid Group on Three Strands
... tions are given for n < 12. Then Le Bruyn in [5] extended all this by establishing such parametrizations for all finite dimensions n, which also generalizes the work of Tuba and Wenzl. Also, researchers gave a great ...
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ON THE IRREDUCIBLITY OF THE REPRESENTATION OF THE PURE BRAID GROUP ON THREE STRANDS
... [2] M. Al-Tahan, M.N. Abdulrahim, A new six dimensional representation of the braid group on three strands and its irreducibility and unitarizability, British J. of Mathematics and Computer Science, 3, No 3 ...
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The Interplay between Linear Representations of the Braid Group
... defined on geometric braids by replacing each string with m strings [2, page 208]. In Section 2 of this paper, we present an infinite series of representations generalizing the standard Artin representation, which were ...
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On Artin's braid group and polyconvexity in the calculus of variations
... listed above occurs in the product; by removing the corresponding word (which is of length either 2, 4 or 6) one arrives at a new product that is again equal to the trivial braid but of length not exceeding m. ...
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Local representations of the loop braid group
... BVSs of group type always extend to loop BVSs, with left group-type BVSs giving representations of and right group-type BVSs giving representations of : De... right group-type then is [r] ...
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Categorifying the sl(2, C) Knizhnik-Zamolodchikov connection via an infinitesimal 2-Yang-Baxter operator in the string Lie-2-algebra
... Let g be a Lie algebra. Let r ∈ g ⊗ g be a symmetric tensor. As men- tioned before, the 4-term relation (1) is implied by the much stronger g- invariance condition (4). In the latter case, the holonomy of the Knizhnik- ...
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Conjugacy in braid groups and the LKB representation : and Bessis Garside groups of rank 3
... In the first section of this chapter we define the faithful representation of the braid group, also known as the Lawrence-Krammer-Bigelow, or LKB representation, and mention some of its properties. In the ...
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New proposals for the popularization of braid theory
... the braid groups. In particular, we give Artin’s description of the braid group in terms of a ...about braid words, one of which is examined in the second part of the ...the braid ...
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Representations of sln(C), the Weyl Group, the Root Lattice, and Linear Braids
... In Chapter 4, we first introduce linear braids, which are certain distinguished lifts from the Weyl group of sl n ( C ) to the braid group, determined by a splitting of the root set of the Weyl ...
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COMPUTING BRAID GROUPS OF GRAPHS WITH APPLICATIONS TO ROBOT MOTION PLANNING
... 3. Each relation says that motions of two robots along disjoint cycles commute. Proof. Computing the 2-point braid group B(G, 2) by Subdivision Theorem 1.4, assume that G has no loops and multiple edges ...
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The Multivariable Alexander Polynomial for a Closed Braid
... ent is a readily constructed multivariable version of the reduced Burau matrices. Other versions of `coloured' Burau matrices have been developed, for example by Penne, 4 ], which can be interpreted as determining linear ...
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Braid groups and quiver mutation
... Since we released the first draft of this article, the preprint [HHLP] has appeared, where the authors give a presentation (different from the one given here) of the Artin braid group for each diagram of ...
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Algorithmic problems in the braid groups
... Consider an n-braid A of the form given in equation 4.43. Suppose we wish to find th e n-braid Am equivalent to A such th a t the length L {A m ) of Am is minim al over the equivalence class of A. It has ...
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5973.pdf
... Rouquier’s braid group action on the category of Soergel bimodules could be extended to a virtual braid group action on a slightly larger category of bimodules which includes not only ...
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139fe7144cbe0cb4e7e2422cc60e634cc1a69ce2.pdf
... triangle groups and the Livn´e lattices in P U (2, 1) is established. Given an elliptic curve E with a puncture at the origin 0, the el- liptic braid group controls its covers equivariant with respect to ...
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Composition problems for braids: Membership, Identity and Freeness
... the braid group inspired a new line of research about the complexity analysis of decision problems for braids, including the word problem, the gen- eralized word problem, root extraction problem, the ...
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