Related papers: Elementary divisors of Cartan matrices for symmetr…
This paper presents an algebraic construction of families of unitary matrices that achieve full diversity. They are obtained as subsets of cyclic division algebras.
We introduce extremely symmetric primes and provide some elementary properties of these.
The paper develops elementary linear algebra methods to compute the determinants of the tensor symmetrizations of quadratic and hermitian forms over fields of good characteristic. Explicit results are given for the partitions $(n)$,…
We examine an elementary problem on prime divisibility of binomial coefficients. Our problem is motivated by several related questions on alternating groups.
Easy quantum groups are compact matrix quantum groups, whose intertwiner spaces are given by the combinatorics of categories of partitions. This class contains the symmetric group and the orthogonal group as well as Wang's quantum…
A method for computing integrals of polynomial functions on compact symmetric spaces is given. Those integrals are expressed as sums of functions on symmetric groups.
Equivalencies of many basic elementary inequalities are given
We introduce a quantum loop group associated to a general symmetric Cartan matrix, by imposing just enough relations between the usual generators $\{e_{i,k}, f_{i,k}\}_{i \in I, k \in \mathbb{Z}}$ in order for the natural Hopf pairing…
We give a new characterization of partial groups as a subcategory of symmetric (simplicial) sets. This subcategory has an explicit reflection, which permits one to compute colimits in the category of partial groups. We also introduce the…
This is the first one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with almost simple linear groups.
We use elementary triangular matrices to obtain some factorization, multiplication, and inversion properties of triangular matrices. We also obtain explicit expressions for the inverses of strict $k$-Hessenberg matrices and banded matrices.…
In this paper we give a Casimir Invariant for the Symmetric group $S_n$. Furthermore we obtain and present, for the first time in the literature, explicit formulas for the matrices of the standard representation in terms of the matrices of…
We develop the generalized Cartan Calculus for the groups $G=$SL$(2,\mathbb{R})\times\mathbb{R}^+$, SL$(5,\mathbb{R})$ and SO(5,5). They are the underlying algebraic structures of $d=9,7,6$ exceptional field theory, respectively. These…
In this paper we will give the computation of the etale fundamental group of an arithmetic scheme.
In this paper we introduce a new type of exponential map in semi-simple compact Lie groups, which is related to the sub-Riemannian geometry generated by the orthogonal complement of a Cartan subalgebra in a similar way to how the group…
We determine the automorphism group of the split Cartan modular curves $X_{\operatorname{split}}(p)$ for all primes $p$.
In this study, we give an alternative and elementary proof to Tsuji's criterion for a Cartier divisor to be numerically trivial.
The purpose of this note is to exhibit some simple and basic constructions for smooth compact transformation groups, and some of their most immediate applications to geometry.
In this paper, we establish Newton-Maclaurin type inequalities for functions arising from linear combinations of primitively symmetric polynomials. This generalization extends the classical Newton-Maclaurin inequality to a broader class of…
In this paper, we give a simple formula for sectional curvatures on the general linear group, which is also valid for many other matrix groups. Similar formula is given for a reductive Lie group. We also discuss the relation between…