Related papers: On Krammer's Representation of the Braid Group
Let $\Pi$ be an irreducible unitary completion of a locally algebraic ${\rm GL}_2(\qp)$-representation. We describe those first-order deformations of $\Pi$ which are themselves completions of a locally algebraic representation. This answers…
We study finite dimensional algebras that appear as fibers of quantum orders over a given point of variety of center. We present the formula for the number of irreducible representations and check it for it for the algebra of twisted…
A class of representations is described for the central extensions, found by Etingof and Frenkel, of current algebras over Riemann surfaces. Their irreducibility is proved. The possibility/impossibility to obtain integrable representations…
Long and Moody gave a method of constructing representations of the braid group B_n. We discuss some ways to generalize their construction. One of these gives representations of subgroups of B_n, including the Gassner representation of the…
The diagram algebra introduced by Brauer that describes the centralizer algebra on tensor products of the natural representation of an orthogonal group has a presentation by generators and relations that only depends on the graph of type An…
These are lecture notes prepared for a minicourse given at the Cimpa Research School "Algebraic and geometric aspects of representation theory", held in Curitiba, Brazil in March 2013. The purpose of the course is to provide an introduction…
We prove that braid group representations associated to braided fusion categories and mapping class group representations associated to modular fusion categories are always semisimple. The proof relies on the theory of extensions in…
The braid group appears in many scientific fields and its representations are instrumental in understanding topological quantum algorithms, topological entropy, classification of manifolds and so on. In this work, we study planer diagrams…
We give an exposition of the work of Bigelow and Krammer who proved that the Artin braid groups are linear.
We construct an infinite tower of irreducible calibrated representations of periplectic Brauer algebras on which the cup-cap generators act by nonzero matrices. As representations of the symmetric group, these are exterior powers of the…
We construct some irreducible representations of the Leavitt path algebra of an arbitrary quiver. The constructed representations are associated to certain algebraic branching systems. For a row-finite quiver, we classify algebraic…
We study a wide range of homologically-defined representations of surface braid groups and of mapping class groups of surfaces, including the Lawrence-Bigelow representations of the classical braid groups. These representations naturally…
We construct the augmentation representation. It is a representation of the fundamental group of the link complement associated to an augmentation of the framed cord algebra. This construction connects representations of two link invariants…
We study the representations of a class of non-commutative polynomial algebras truncated at degree 3, with one additional relation. We determine the irreducible components of their varieties of representations. We do this by showing that…
This is a survey paper about affine Hecke algebras. We start from scratch and discuss some algebraic aspects of their representation theory, referring to the literature for proofs. We aim in particular at the classification of irreducible…
We construct a [(n+1)/2]+1 parameters family of irreducible representations of the Braid group B_3 in arbitrary dimension n\in N, using a q-deformation of the Pascal triangle. This construction extends in particular results by S.P.Humphries…
Quantum monodromy matrices coming from a theory of two coupled (m)KdV equations are modified in order to satisfy the usual Yang-Baxter relation. As a consequence, a general connection between braided and {\it unbraided} (usual) Yang-Baxter…
In this note we first consider a ternary matrix group related to the von Neumann regular semigroups and to the Artin braid group (in an algebraic way). The product of a special kind of ternary matrices (idempotent and of finite order)…
We investigate the braid group representations arising from categories of representations of twisted quantum doubles of finite groups. For these categories, we show that the resulting braid group representations always factor through finite…
We show that the two coproducts of a Markov $L$-coalgebra yield at least two solutions of the Yang-Baxter equation and thus at least two representations of braid groups.