Related papers: The Exponential Map for the Conformal Group 0(2,4)

The complete classification of the finite simple groups that are $(2,3)$-generated is a problem which is still open only for orthogonal groups. Here, we construct $(2, 3)$-generators for the finite odd-dimensional orthogonal groups…

Let $G$ be a simple and simply connected algebraic group over an algebraically closed field $\Bbbk$ of characteristic $p>0$. Assume that $p$ is good for the root system of $G$ and that the covering map $G_{sc} \rightarrow G$ is separable.…

A variational integrator of arbitrarily high-order on the special orthogonal group $SO(n)$ is constructed using the polar decomposition and the constrained Galerkin method. It has the advantage of avoiding the second-order derivative of the…

In this thesis, we construct a new version of orthogonal calculus for functors $F$ from $C_2$-representations to $C_2$-spaces, where $C_2$ is the cyclic group of order 2. For example, the functor $BO(-)$, which sends a $C_2$-representation…

We give a new technique for constructing presentations by generators and relations for representations of groups like $SL_n(\mathbb{Z})$ and $Sp_{2g}(\mathbb{Z})$. Our results play an important role in recent work of the authors calculating…

We consider the Macdonald group $\langle x,y\,|\, x^{[x,y]}=x^{1+2^m\ell},\, y^{[y,x]}=y^{1+2^m\ell}\rangle$ and its Sylow 2-subgroup $J=\langle x,y\,|\, x^{[x,y]}=x^{1+2^m\ell},\, y^{[y,x]}=y^{1+2^m\ell},…

In this paper we present a new procedure to obtain unitary and irreducible representations of Lie groups starting from the cotangent bundle of the group (the cotangent group). We discuss some applications of the construction in…

We provide an algorithm to compute generators of the orthogonal group of the discriminant group associated to an integral quadratic lattice over the integers. We give a closed formula for its order.

We show that the mapping class group of an orientable finite type surface has uniformly exponential growth, as well as various closely related groups. This provides further evidence that mapping class groups may be linear.

All indecomposable finite-dimensional representations of the homogeneous Galilei group which when restricted to the rotation subgroup are decomposed to spin 0, 1/2 and 1 representations are constructed and classified. These representations…

We construct generators of the center of the universal enveloping algebra of the complex orthogonal Lie algebra realized as the alternative matrices of size $n$. These elements are constructed in accordance with the Iwasawa decomposition of…

Zhao and the second author (2013) constructed a functor from o(k)-Mod to o(k + 2)-Mod. In this paper, we use the functor successively to obtain an universal first-order differential operator realization for any highest-weight representation…

We show for g > 6 that the second homology group of the Torelli group of a surface of genus g and 1 boundary component is generated as an Sp(2g,Z)-module by the image under the stabilization map of the second homology group of the Torelli…

In this paper we revisit the concept of conformality in the sense of Gauss in the context of octonions and Clifford algebras. We extend a characterization of conformality in terms of a system of partial differential equations and…

We consider conformally invariant energies $W$ on the group $\operatorname{GL}^+(2)$ of $2\times2$-matrices with positive determinant, i.e. $W\colon\operatorname{GL}^+(2)\to\mathbb{R}$ such that \[W(AFB) = W(F) \qquad\text{for all }\;…

We first review some invariant theoretic results about the finite subgroups of SU(2) in a quick algebraic way by using the McKay correspondence and quantum affine Cartan matrices. By the way it turns out that some parameters (a,b,h;p,q,r)…

Let $(\X,\omega)$ be a compact symplectic orbifold. We define $\pi_1(Ham(\X, \omega))$, the fundamental group of the 2-group of Hamiltonian diffeomorphisms of $(\X, \omega)$, and construct a group homomorphism from $\pi_1(Ham(\X, \omega))$…

Matrices of the irreducible representations of double crystallographic point groups O, Td, Ox{1,I} and Tdx{1,I} are derived. The characteristic polynomials (spinor bases) up to the sixth power are obtained. The method for the derivation of…

In this paper, we study matricial representations of certain finitely presented groups with N-generators of order-2. As an application, we consider a group algebra under our representations. Specifically, we characterize the inverses of all…

The observation that n pairs of para-Fermi (pF) operators generate the universal enveloping algebra of the orthogonal Lie algebra so(2n+1) is used in order to define deformed pF operators. It is shown that these operators are an alternative…