Related papers: A method for building permutation representations …
In this paper we give an algorithm to determine all finite matrix groups over a number field. Our algorithm is based on the representation theory of finite groups.
The action of a finite reflection group (type A) on its set of roots is understood as a permutation representation or group action. We show that this representation is an induced representation from a certain kind of parabolic subgroup.…
We present a novel preconditioning technique for proximal optimization methods that relies on graph algorithms to construct effective preconditioners. Such combinatorial preconditioners arise from partitioning the graph into forests. We…
In this short paper we present an algorithm for finding a solution to a generalized Sudoku.
We obtain a new representation for the partition function of the six vertex model with domain wall boundaries using a functional equation recently derived by the author. This new representation is given in terms of a sum over the…
A long-term research proposal on the algebraic structure, the representations and the possible applications of paraparticle algebras is structured in three modules: The first part stems from an attempt to classify the inequivalent gradings…
Mathematical core of quantum mechanics is the theory of unitary representations of symmetries of physical systems. We argue that quantum behavior is a natural result of extraction of "observable" information about systems containing…
We generalize the Plesken-Fabia\'nska $\mathrm{L}_2$-quotient algorithm for finitely presented groups on two or three generators to allow an arbitrary number of generators. The main difficulty lies in a constructive description of the…
Gaussian unitary transformations are generated by quadratic Hamiltonians, i.e., Hamiltonians containing quadratic terms in creations and annihilation operators, and are heavily used in many areas of quantum physics, ranging from quantum…
We present a property satisfied by a large variety of complex continued fraction algorithms (the "finite building property") and use it to explore the structure of bijectivity domains for natural extensions of Gauss maps. Specifically, we…
Irreducible representations (irreps) of a finite group $G$ are equivalent if there exists a similarity transformation between them. In this paper, we describe an explicit algorithm for constructing this transformation between a pair of…
Porous structures are intricate solid materials with numerous small pores, extensively used in fields like medicine, chemical engineering, and aerospace. However, the design of such structures using computer-aided tools is a time-consuming…
We give a review of modern approaches to constructing formal solutions to integrable hierarchies of mathematical physics, whose coefficients are answers to various enumerative problems. The relationship between these approaches and…
A method of Proctor [European J. Combin. 5 (1984), no. 4, 331-350] realizes the set of arbitrary plane partitions in a box and the set of symmetric plane partitions as bases of linear representations of Lie groups. We extend this method by…
Let $F$ be a local non-archimedian field of positive characteristic, $D$ be a skew-field with center $F$ and $ G=D^{\star}$ be the multiplicative group of $D$. The goal of this paper is to provide a canonical decomposition of any complex…
A real representation of a finite group naturally determines a polytope, generalizing the well-known Birkhoff polytope. This paper determines the structure of the polytope corresponding to the natural permutation representation of a general…
Various descending chains of subgroups of a finite permutation group can be used to define a sequence of `basic' permutation groups that are analogues of composition factors for abstract finite groups. Primitive groups have been the…
We investigate the question which Q-valued characters and characters of Q-representations of finite groups are Z-linear combinations of permutation characters. This question is known to reduce to that for quasi-elementary groups, and we…
We start with a small paradigm shift about group representations, namely the observation that restriction to a subgroup can be understood as an extension-of-scalars. We deduce that, given a group $G$, the derived and the stable categories…
This paper is devoted to the proof of a structural theorem, concerning certain homomorphic images of Artin braid group on $n$ strands in finite symmetric groups. It is shown that any one of these permutation groups is an extension of the…