$N$-Dimensional Representations of the Braid Groups $B_{N}$

For any n>3, we give a family of finite dimensional irreducible representations of the braid group B_n. Moreover, we give a subfamily parametrized by 0<m<n of dimension the combinatoric number (n,m). The representation obtained in the case m=1 is equivalent to the Standard representation.

This note tells you how to construct a k(n)-dimensional family of (isomorphism classes of) irreducible representations of dimension n for the three string braid group B_3, where k(n) is an admissible function of your choosing; for example take k(n) = [ n/2 ] +1 as in arXiv:0803.2778 and arXiv:0803.2785.

In this paper we study irreducible matrix representations of the welded braid group $WB_n$, also known as the group of conjugating automorphisms of a free group $F_n.$ We prove that $WB_n$ has no irreducible representations of dimension $r,$ where $2\leqslant r\leqslant n-2$ for $n\geqslant 5.$ We give complete classification of all extensions of irreducible representations of the braid group $B_n$ to the welded braid group $WB_n$ of dimensions $n-1$ (for $n\geqslant 7$) and ...

In this paper the author finds explicitly all finite-dimensional irreducible representations of a series of finite permutation groups that are homomorphic images of Artin braid group.

We give a method to produce representations of the braid group $B_n$ of $n-1$ generators ($n\leq \infty$). Moreover, we give sufficient conditions over a non unitary representation for being of this type. This method produces examples of irreducible representations of finite and infinite dimension.

In 1996 E. Formanek classified all the irreducible complex representations of $B_n$ of dimension at most $n-1,$ where $B_n$ is the Artin braid group on $n$ strings. In this paper we extend this classification to the representations of dimension $n,$ for $n\geq 9$. We prove that all such representations are equivalent to a tensor product of a one-dimensional representation and a specialization of a certain one-parameter family of $n-$dimensional representations, that was first...

This paper is the first part of a series of papers aimed at improving the classification by Formanek of the irreducible representations of Artin braid groups of small dimension. In this paper we classify all the irreducible complex representations $\rho$ of Artin braid group $B_n$ with the condition $rank (\rho (\sigma_i)-1)=2$ where $\sigma_i$ are the standard generators. For $n \geq 7$ they all belong to some one-parameter family of $n$-dimensional representations.

Burau representation of the Artin braid group remains as one of the very important representations for the braid group. Partly, because of its connections to the Alexander polynomial which is one of the first and most useful invariants for knots and links. In the present work, we show that interesting representations of braid group could be achieved using a simple and intuitive approach, where we simply analyse the path of strands in a braid and encode the over-crossings, und...

In [1] we have constructed a [n+1/2]+1 parameters family of irreducible representations of the Braid group B_3 in arbitrary dimension using a $q-$deformation of the Pascal triangle. This construction extends in particular results by S.P. Humphries (2000), who constructed representations of the braid group B_3 in arbitrary dimension using the classical Pascal triangle. E. Ferrand (2000) obtained an equivalent representation of B_3 by considering two special operators in the sp...

We list the irreducible two dimensional complex representations of the Braid group B3 in elementary way. Then, we make a decomposition of the square of its irreducible Burau representation.