Related papers: Extraspecial 2-groups and images of braid group re…
We give several formulas for the character of an arbitrary irreducible finite--dimensional representation for the Yangian of sl_2.
Using a theorem of Schechtman - Varchenko on integral expressions for solutions of Knizhnik - Zamolodchikov equations we prove that the solutions of the Yang - Baxter equation associated to complex simple Lie algebras belong to the class of…
Let B be the generalized braid group associated to some finite complex reflection group. We define a representation of B of dimension the number of reflections of the corresponding reflection group, which generalizes the Krammer…
The Yang-Baxter equation (YBE) and the reflection equation (RE) both come from mathematical physics, and they can be defined in any monoidal category. For cartesian monoidal categories, we prove that every solution to the RE provides a…
A new class of indecomposable, irretractable, involutive, non-degenerate set-theoretic solutions of the Yang--Baxter equation is constructed. This class complements the class of such solutions constructed in \cite{CO22} and together they…
Braid groups may be defined for every Coxeter diagram. Artin's braid group is of type A. Analogs of Temperley-Lieb, Hecke and Birman-Wenzl algebras exist for B-type. Our general hypothethis is that the braid group of B-type replaces Artin's…
This paper is devoted to the proof of a structural theorem, concerning certain homomorphic images of Artin braid group on $n$ strands in finite symmetric groups. It is shown that any one of these permutation groups is an extension of the…
There exists a multiplicative homomorphism from the braid group B to the Temperley-Lieb algebra TL. Moreover, the homomorphic images in TL of the simple elements form a basis for the vector space underlying TL. In analogy with the case of…
We study solutions of the Yang-Baxter equation on a tensor product of an arbitrary finite-dimensional and an arbitrary infinite-dimensional representations of the rank one symmetry algebra. We consider the cases of the Lie algebra sl_2, the…
Supersymmetry algebras can be used to obtain algebraic expressions for constant Yang-Baxter solutions, also known as braid group generators. This was done for non-invertible braid operators in \cite{maity2025non}. In this work we extend…
We develop a theory of localization for braid group representations associated with objects in braided fusion categories and, more generally, to Yang-Baxter operators in monoidal categories. The essential problem is to determine when a…
All polynomial invariants of links for two dimensional solutions of Yang-Baxter equation is constructed by employing Turaev's method. As a consequence, it is proved that the best invariant so constructed is the Jones polynomial and there…
The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional…
In this note, a new class of representations of the braid groups $B_{N}$ is constructed. It is proved that those representations contain three kinds of irreducible representations: the trivial (identity) one, the Burau one, and an…
The Artin exponent induced from cyclic subgroups of finite groups was studied extensively by T.Y. Lam. A Burnside ring theoretic version of Lam's results for $p$-groups was given by the author in an earlier paper. Here we look at the Artin…
Towards the study of the representation theory of any dihedral Artin group B, we build rational morphisms from B to the group of invertible elements of the associated infinitesimal braids algebra. For this we build analogues of Drinfeld…
We consider the irreducible representations each of dimension 2 of the necklace braid group $\mathcal{NB}_n$ ($n=2,3,4$). We then consider the tensor product of the representations of $\mathcal{NB}_n$ ($n=2,3,4$) and determine necessary and…
We determine the finite groups whose real irreducible representations have different degrees.
Braided algebras are associative algebras endowed with a Yang-Baxter operator that satisfies certain compatibility conditions involving the multiplication. Along with Hochschild cohomology of algebras, there is also a notion of Yang-Baxter…
We study the complex irreducible representations of special linear, symplectic, orthogonal and unitary groups over principal ideal local rings of length two. We construct a canonical correspondence between the irreducible representations of…