Related papers: SgpDec: Cascade (De)Compositions of Finite Transfo…

By a 2-group we mean a groupoid equipped with a weakened group structure. It is called split when it is equivalent to the semidirect product of a discrete 2-group and a one-object 2-group. By a permutation 2-group we mean the 2-group…

We present a new version of $\texttt{SecDec}$, a program for the numerical computation of parametric integrals in the context of dimensional regularization. By its modular structure, the $\texttt{python}$ rewrite $\texttt{pySecDec}$ is much…

SecDec is a program which can be used for the evaluation of parametric integrals, in particular multi-loop integrals. For a given set of propagators defining the graph, the program constructs the graph polynomials, factorizes the endpoint…

The wreath product of two permutation groups G < Sym(Gamma) and H < Sym(Delta) can be considered as a permutation group acting on the set Pi of functions from Delta to Gamma. This action, usually called the product action, of a wreath…

We present pySecDec, a new version of the program SecDec, which performs the factorisation of dimensionally regulated poles in parametric integrals, and the subsequent numerical evaluation of the finite coefficients. The algebraic part of…

We investigate a semigroup construction generalising the two-sided wreath product. We develop the foundations of this construction and show that for groups it is isomorphic to the usual wreath product. We also show that it gives a slightly…

We introduce the concept of deck transformations within the category of developable complexes of groups. Drawing inspiration from classical covering theory for topological spaces, we propose an alternative construction of the universal…

We describe a general technique for embedding certain amalgamated products into direct products. This technique provides us with a way of constructing a host of finitely presented subgroups of automatic groups which are not even…

The blow-up construction by L. G. Kov\'acs has been a very useful tool to study embeddings of finite primitive permutation groups into wreath products in product action. In the present paper we extend the concept of a blow-up to finite…

Normal subgroups and there properties for finite and infinite iterated wreath products $S_{n_1}\wr \ldots \wr S_{n_m}$, $n, m \in \mathbb{N}$ are founded. The special classes of normal subgroups and there orders are investigated. Special…

Let X be an algebraic variety with an action of an algebraic group G. Suppose X has a full exceptional collection of sheaves, and these sheaves are invariant under the action of the group. We construct a semiorthogonal decomposition of…

To a finite group G one can associate a tower of wreath products S_n[G]. It is well known that the graded direct sum of the Grothendieck groups of the categories of finite dimensional complex representations of these groups can be given the…

The aim of this work is to reduce the complexity of the available algorithms for computing the generator sets of a semigroup ideal by using the Hermite normal form. In order to achieve it we introduce the concept of decomposable semigroup.…

A constructive method for decomposing finite dimensional representations of semisimple real Lie algebras is developed. The method is illustrated by an example. We also discuss an implementation of the algorithm in the language of the…

Let I be a finite partially ordered set and let (Sym({\Delta}i),{\Delta}i)i be a sequence of symmetric groups indexed by I. Construct the generalised wreath product (F, {\Delta}) on this sequence of permutation groups. We determine the…

Diagram semigroups are interesting algebraic and combinatorial objects, several types of them originating from questions in computer science and in physics. Here we describe diagram semigroups in a general framework and extend our…

Given a finite group $\Gamma$ and a virtual character $\wt$ on it, we construct a Fock space and associated vertex operators in terms of representation ring of wreath products $\Gamma\sim S_n$. We recover the character tables of wreath…

We present an application of the program of groupoidification leading up to a sketch of a categorification of the Hecke algebroid --- the category of permutation representations of a finite group. As an immediate consequence, we obtain a…

In this paper we propose an alternative construction of a certain class of Deformed Double Current Algebras. We construct them as spherical subalgebras of symplectic reflection algebras in the Deligne category. They can also be thought of…

We describe the structure of the irreducible representations of crossed products of unital C*-algebras by actions of finite groups in terms of irreducible representations of the C*-algebras on which the groups act. We then apply this…