Related papers: Mutation classes of skew-symmetrizable 3x3 matrice…
We study Fomin-Zelevinsky's mutation rule in the context of noncrystallographic root systems. In particular, we construct approximately periodic sequences of real numbers for the noncrystallographic root systems of rank 2 by adjusting the…
We compute two-term skein modules of framed oriented links in oriented 3-manifolds. They contain the self-writhe and total linking number invariants of framed oriented links in a universal way. The relations in a natural presentation of the…
We perform the group analysis of Witten's equations of motion for a particle moving in the presence of a magnetic monopole, and also when constrained to move on the surface of a sphere, which is the classical Wess-Zumino-Witten model. We…
Multiplicative analogues of the shuffle elements of the braid group rings are introduced; in local representations they give rise to certain graded associative algebras (b-shuffle algebras). For the Hecke and BMW algebras, the…
In the present paper we show a link between bistochastic quantum channels and classical maps. The primary goal of this work is to analyse the multiplicative structure of the Birkhoff polytope of order 3 (the simplest non-trivial case). A…
The process of alternately row scaling and column scaling a positive $n \times n$ matrix $A$ converges to a doubly stochastic positive $n \times n$ matrix $S(A)$, often called the \emph{Sinkhorn limit} of $A$. The main result in this paper…
We simplify and extend our previous model for the masses and mixing matrix of three Majorana neutrinos based on permutation symmetry $S_3$ and the perturbations which violate this symmetry. The perturbations are arranged such that we get…
In recent work, robust mixture modelling approaches using skewed distributions have been explored to accommodate asymmetric data. We introduce parsimony by developing skew-t and skew-normal analogues of the popular GPCM family that employ…
The least upper bound on degrees of elements of a minimal system of generators of the algebra of invariants of 3x3 matrices is found, and the nilpotency degree of a relatively free finitely generated algebra with the identity x^3=0 is…
This paper concerns the enumeration of simultaneous conjugacy classes of tuples of commuting unitary matrices and of commuting symplectic matrices over a finite field $\mathbf{F}_q$ of odd size. For any given conjugacy class, the orbits for…
For a compact surface $S = S_{g,n}$ with $3g + n \geq 4$, we introduce a family of unitary representations of the mapping class group Mod($S$) based on the space of measured foliations. For this family of representations, we show that none…
An algebra is called skew-symmetric if its multiplication operation is a skew-symmetric bilinear application. We determine all these algebras in dimension $3$ over a field of characteristic different from $2$. As an application, we…
We investigate the breaking of SU(3) into its subgroups from the viewpoints of explicit and spontaneous breaking. A one-to-one link between these two approaches is given by the complex spherical harmonics, which form a complete set of…
In this paper, we deal with stable homology computations with twisted coefficients for mapping class groups of surfaces and of 3-manifolds, automorphism groups of free groups with boundaries and automorphism groups of certain right-angled…
This paper investigates the equivalence reduction for several classes of multivariate polynomial matrices and their Smith forms, establishing some criteria for such reduction. In particular, we employ algebra isomorphisms as a key tool to…
We extend the existing skew polynomial representations of matrix algebras which are direct sum of matrix spaces over division rings. In this representation, the sum-rank distance between two tuples of matrices is captured by a weight…
Although the conjugacy classes of the general linear group are known, it is not obvious (from the canonic form of matrices) that two permutation matrices are similar if and only if they are conjugate as permutations in the symmetric group,…
Consider a semi-infinite skew-symmetric moment matrix, $m_{\iy}$ evolving according to the vector fields $\pl m / \pl t_k=\Lb^k m+m \Lb^{\top k} ,$ where $\Lb$ is the shift matrix. Then the skew-Borel decomposition $ m_{\iy}:= Q^{-1} J…
Discrete symmetries being preferred to explain the neutrino phenomenology, we chose the simplest $S_3$ group and explore the implication of its modular form on neutrino masses and mixing. Non-trivial transformations of Yukawa couplings…
We define and investigate a family of permutations matrices, called shuffling matrices, acting on a set of $N=n_1\cdots n_m$ elements, where $m\geq 2$ and $n_i\geq 2$ for any $i=1,\ldots, m$. These elements are identified with the vertices…