Related papers: An algebraic approach to representations of the pe…
A simple procedure to obtain complete, closed expressions for Lie algebra invariants is presented. The invariants are ultimately polynomials in the group parameters. The construction of finite group elements require the use of projectors,…
A model of representations of a Lie algebra is a representation which a direct sum of all irreducible finite dimensional representations taken with multiplicity $1$. In the paper an explicit construction of a model of representation for all…
Questions at the intersection of the AdS/CFT correspondence and quantum information theory motivate the study of projectors in sequences of subalgebras of finite-dimensional commutative associative semisimple algebras $\mathcal{A}$,…
The study of images of noncommutative polynomials on algebras has attracted considerable attention. We investigate polynomial images and the additive structures they generate in associative algebras, focusing on sums and products of values.…
We derive a formula for the entries in the change-of-basis matrix between Young's seminormal and natural representations of the symmetric group. These entries are determined as sums over weighted paths in the weak Bruhat graph on standard…
The orthogonal groups are a series of simple Lie groups associated to symmetric bilinear forms. There is no analogous series associated to symmetric trilinear forms. We introduce an infinite dimensional group-like object that can be viewed…
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…
The decomposition matrix of a finite group in prime characteristic p records the multiplicities of its p-modular irreducible representations as composition factors of the reductions modulo p of its irreducible representations in…
Denote the alternating and symmetric groups of degree $n$ by $A_n$ and $S_n$ respectively. Consider a permutation $\sigma\in S_n$ all of whose nontrivial cycles are of the same length. We find the minimal polynomials of $\sigma$ in the…
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 partition algebras are algebras of diagrams (which contain the group algebra of the symmetric group and the Brauer algebra) such that the multiplication is given by a combinatorial rule and such that the structure constants of the…
We study the representation theory of the uniform block permutation algebra in the context of the representation theory of factorizable inverse monoids. The uniform block permutation algebra is a subalgebra of the partition algebra and is…
An approach to representations of finite groups is presented without recourse to character theory. Considering the group algebra C[G] as an algebra of linear maps on C[G] (by left multiplication), we derive the primitive central idempotents…
Let F be the field of two elements and G a finite abelian 2-group with an involutory automorphism. The extension of this automorphism to the group algebra FG is called an involutory involution. This determines the groups of unitary and…
We develop a new, group-theoretic approach to bounding the exponent of matrix multiplication. There are two components to this approach: (1) identifying groups G that admit a certain type of embedding of matrix multiplication into the group…
Group algebras of permutations have proved highly useful in solving a number of problems in large N gauge theories. I review the use of permutations in classifying gauge invariants in one-matrix and multi-matrix models and computing their…
We give an elementary analysis of the multiplicator group of the Galilei group in 1+2 dimensions $G^{\uparrow}_{+}$. For a non-trivial multiplicator we give a list of all the corresponding projective unitary irreducible representations of…
This paper proposes a new approach to deriving a finite particle content, suitable for the construction of a gauge theory. Specifically, the outlined construction generates a finite set of irreducible gauge representations, which are…
The projective line over a field carries structure of a groupoid with a certain correspondence between objects and arrows. We discuss to what extent the field can be reconstructed from the groupoid.
The objective of this paper is to determine the finite dimensional, indecomposable representations of the algebra that is generated by two complex structures over the real numbers. Since the generators satisfy relations that are similar to…