Related papers: Constructive homomorphisms for classical groups

In this note, we establish an equivalence of categories between the category of all eight-dimensional composition algebras with any given quadratic form $n$ over a field $k$ of characteristic not two, and a category arising from an action…

Monodromy in analytic families of smooth complex surfaces yields groups of isotopy classes of orientation preserving diffeomorphisms for each family member X. For all deformation classes of minimal elliptic surfaces with p_g>q=0, we…

Let $\Omega$ denote a non-empty finite set. Let $S(\Omega)$ stand for the symmetric group on $\Omega$ and let us write $P(\Omega)$ for the power set of $\Omega$. Let $\rho: S(\Omega) \to U(L^2(P(\Omega)))$ be the left unitary representation…

This paper is a significant part of a general project aimed to classify all irreducible representations of finite quasi-simple groups over an algebraically closed field, in which the image of at least one element is represented by an almost…

Constructing complex computation from simpler building blocks is a defining problem of computer science. In algebraic automata theory, we represent computing devices as semigroups. Accordingly, we use mathematical tools like products and…

Heisenberg groups over algebras with central involution and their automorphism groups are constructed. The complex quaternion group algebra over a prime field is used as an example. Its subspaces provide finite models for each of the real…

We construct spherical subgroups in infinite-dimensional classical groups $G$ (usually they are not symmetric and their finite-dimensional analogs are not spherical). We present a structure of a semigroup on double cosets $L\setminus G/L$…

In this paper we develop a formalism for working with twisted realizations of vertex and conformal algebras. As an example, we study realizations of conformal algebras by twisted formal power series. The main application of our technique is…

Let $G$ be a finite solvable group, given through a refined consistent polycyclic presentation, and $\alpha$ an automorphism of $G$, given through its images of the generators of $G$. In this paper, we discuss algorithms for computing the…

The regular objects in various categories, such as maps, hypermaps or covering spaces, can be identified with the normal subgroups N of a given group \Gamma, with quotient group isomorphic to \Gamma/N. It is shown how to enumerate such…

For all classical groups (and for their analogs in infinite dimension or over general base fields or rings) we construct certain contractions, called "homotopes". The construction is geometric, using as ingredient involutions of associative…

For all classical groups (and for their analogs in infinite dimension or over general base fields or rings) we construct certain contractions, called "homotopes". The construction is geometric, using as ingredient involutions of associative…

We represent vector bundles over a regular algebraic curve as pairs of lattices over the maximal orders of its function field and we give polynomial time algorithms for several tasks: computing determinants of vector bundles, kernels and…

Let $\Gamma$ be a crystallographic group of dimension $n,$ i.e. a discrete, cocompact subgroup of $\operatorname{Isom}(\mathbb{R}^n)$ = $O(n)\ltimes\mathbb{R}^n.$ For any $n\geq 2,$ we construct a crystallographic group with a trivial…

Recent results by Harrow et. al. and by Ta-Shma, suggest that quantum computers may have an exponential advantage in solving a wealth of linear algebraic problems, over classical algorithms. Building on the quantum intuition of these…

We show that a pair of complementary dagger-Frobenius algebras, equipped with a self-conjugate comonoid homomorphism onto one of the algebras, produce a nontrivial unitary morphism on the product of the algebras. This gives an abstract…

We prove that extension groups in strict polynomial functor categories compute the rational cohomology of classical algebraic groups. This result was previously known only for general linear groups. We give several applications to the study…

Given a simplicial complex $X$, we construct a simplicial complex $\Omega X$ that may be regarded as a combinatorial version of the based loop space of a topological space. Our construction explicitly describes the simplices of $\Omega X$…

We present the ideas behind an algorithm to compute normalizers of primitive groups with non-regular socle in polynomial time. We highlight a concept we developed called permutation morphisms and present timings for a partial implementation…

First, we give a functorial construction of a group associated to a symmetric operad. Applied to the endomorphism operad it gives the group of formal diffeomorphisms. Second, we associate a symmetric operad to any family of decorated graphs…