Related papers: Elementary divisors of Cartan matrices for symmetr…
The aim of this article is to draw attention towards various natural but unanswered questions related to the lower central series of the unit group of an integral group ring.
We develop symmetric Cartan calculus, an analogue of classical Cartan calculus for symmetric differential forms. We first show that the analogue of the exterior derivative, the symmetric derivative, is not unique and its different choices…
This is an essay about a certain family of elements in the general linear group GL(d,q) called primitive prime divisor elements, or ppd-elements. A classification of the subgroups of GL(d,q) which contain such elements is discussed, and the…
We give an elementary proof of the group law for elliptic curves using explicit formulas.
The purpose of this note is to extend in a simple and unified way the known results on interlacing of zeros of paraorthogonal polynomials on the unit circle. These polynomials can be regarded as the characteristic polynomials of any matrix…
Partition functions for dimers on closed oriented surfaces are known to be alternating sums of Pfaffians of Kasteleyn matrices. In this paper, we obtain the formula for the coefficients in terms of discrete spin structures.
Commutators and anticommutators of gamma matrices with arbitrary numbers of (antisymmetrized) indices are derived.
The main purpose of this paper is providing a simple method to generate the matrices of irreducible representations because it is useful to reduce the computational time of solving the eigenvalue problems. The only information we need to…
The goal of this paper is to develop a systematic method of locating the Mueller matrices within the class of the matrices of the real group SL(4, R). The main idea is to construct the general transformation of the group SL(4, R) (whose…
A {\it symmetric companion matrix} is a matrix of the form $A +A^T$ where $A$ is a companion matrix all of whose entries are in $\{0,1\}$ and $A^T$ is the transpose of $A.$ In this paper, we find the total number of primitive and the total…
We find an algorithmic procedure that enables to compute and to describe the structure of the isotropy subgroups of the group of complex orthogonal matrices with respect to the action of similarity on complex symmetric matrices. A key step…
The main purpose of this paper is to introduce the structure of soft group category. In this category, we determine some special objects and morphisms having a universal structure such as the final object and product. Therefore, the…
A new matrix operation based on inserting columns and rows, similarly to the mediant operation between fractions, gives rise to the Farey determinants matrix or, equivalently, the matrix of the numerators of the differences of Farey…
In this paper we investigate the spectrum of the differential operators generated by the ordinary differential expression of odd order with PT-symmertic periodic matrix coefficients
An elementary approach to the construction of Coxeter group representations is presented.
This paper contains a complete description of classes of the unitary equivalence of the admissible representations of infinite-dimensional classic matrix groups paper.
A general method for calculating or constructing lower central factors of groups is presented. {\it Relative basic commutators} are defined.
A very simple and short proof of the polynomial matrix spectral factorization theorem (on the unit circle as well as on the real line) is presented, which relies on elementary complex analysis and linear algebra.
This is the second one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with almost simple unitary groups.
We present a simple approach to discrete q-Hermite polynomials with special emphasis on analogies with the classical case.