Related papers: On Krammer's Representation of the Braid Group
We use $q$-Pascal's triangle to define a family of representations of dimension 6 of the braid group $B_3$ on three strings. Then we give a necessary and sufficient condition for these representations to be irreducible.
We continue to investigate branching systems of directed graphs and their connections with graph algebras. We give a sufficient condition under which the representation induced from a branching system of a directed graph is faithful and…
We characterize group representations that factor through monomial representations, respectively, block-triangular representations with monomial diagonal blocks, by arithmetic properties. Similar results are obtained for semigroup…
We investigate a family of (reducible) representations of Artin's braid groups corresponding to a specific solution to the Yang-Baxter equation. The images of the braid groups under these representations are finite groups, and we identify…
In this note, we initiate a study of the finite-dimensional representation theory of a class of algebras that correspond to noncommutative deformations of compact surfaces of arbitrary genus. Low dimensional representations are investigated…
We discuss permutation representations which are obtained by the natural action of $S_n \times S_n$ on some special sets of invertible matrices, defined by simple combinatorial attributes. We decompose these representations into…
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 show that representations of the loop braid group arise from Aharonov-Bohm like effects in finite 2-group (3+1)-dimensional topological higher gauge theory. For this we introduce a minimal categorification of biracks, which we call…
We introduce a new Baxterisation for R-matrices that depend separately on two spectral parameters. The Baxterisation is based on a new algebra, close to but different from the braid group. This allows us to recover the R-matrix of the…
We use the notion of Bridgeland stability condition and its associated metric to endow triangulated categories with extriangulated structures and study their extriangulated Grothendieck groups. This study is motivated by Khovanov-Seidel's…
We construct representation theory of Lie algebras with filtrations. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are found.
In this paper we prove certain Hurwitz equivalence properties in the braid group. Our main result is that every two factorizations of $\Delta_n ^2$ where the elements of the factorization are semi-frame are Hurwitz equivalent. The results…
In this paper we consider symmetric powers representation and exterior powers representation of finite groups, which generated by the representation which has finite dimension over the complex field. We calculate the multiplicity of…
We investigate the Bieri--Neumann--Strebel--Renz (BNSR) invariants of irreducible uniform lattices. In the case of a direct product of a tree and a Euclidean space we show that vanishing of the BNSR invariants for all finite-index subgroups…
The Eulerian idempotents, first introduced for the symmetric group and later extended to all reflection groups, generate a family of representations called the Eulerian representations that decompose the regular representation. In Type $A$,…
In this short note we show that every connected reductive simply-connected algebraic group of rank $>1$ over the complex numbers has infinitely many pairs of irreducible representations which are not related by an automorphism of the…
The group algebra of the permutation group is spanned by a set of elements called projectors. The coordinates of permutations expanded in projectors are matrix elements of irreducible representations. The projectors of the permutation group…
We describe the structure of the irreducible representations of crossed products of unital C*-algebras by actions of finite groups in terms of irreducible representations of the C*-algebras on which the groups act. We then apply this…
In this paper, we go on Rui-Xu's work on cyclotomic Birman-Wenzl algebras $\W_{r, n}$ in \cite{RX}. In particular, we use the representation theory of cellular algebras in \cite{GL} to classify the irreducible $\W_{r, n}$-modules for all…
In this paper, we calculate decomposition matrices of the Birman-Murakami-Wenzl algebras over $\mathbb C$.