Related papers: Brauer relations in finite groups

Let $N$ be a normal subgroup of a finite group $G$. From a result due to Brauer, it can be derived that the character table of $G$ contains square submatrices which are induced by the $G$-conjugacy classes of elements in $N$ and the…

For each prime p, we exhibit pairs of p-groups all of whose integral cohomology groups are isomorphic. The method used involves very little calculation. The groups are exhibited as kernels of homomorphisms from a compact Lie group G to…

This paper aims to determine the images of the braid group under representations afforded by the Yang Baxter equation when the solution is a nontrivial $4 \times 4$ matrix. Making the assumption that all the eigenvalues of the Yang Baxter…

In this paper, we define and study a kind of Steinberg representation for linear algebraic groups of a particular kind, called groups of parahoric type, defined overa finite field; in particular, when G is the group of F-points of a…

Let $V$ be a finite rank vector space over a perfect field of characteristic $p>0$, and let $G$ be a finite subgroup of $\operatorname{GL}(V)$. If $V$ is a permutation representation of $G$, or more generally a monomial representation, we…

This thesis addresses questions in representation and invariant theory of finite groups. The first concerns singularities of quotient spaces under actions of finite groups. We introduce a class of finite groups such that the quotients have…

For finite groups $G$ with non-abelian, trivial intersection Sylow $p$-subgroups, the analysis of the Loewy structure of the centre of a block allows us to deduce that a stable equivalence of Morita type does not induce an algebra…

We introduce partial representation of a finite groupoid $G$ on an algebra $A$ and show that the partial groupoid representations of $G$ are in one-to-one correspondence with the representations of the algebra generated by the Birget-Rhodes…

We study the representations of the commutator subgroup K_{n} of the braid group B_{n} into a finite group . This is done through a symbolic dynamical system. Some experimental results enable us to compute the number of subgroups of K_{n}…

In this article, we classify disconnected reductive groups over an algebraically closed field with a few caveats. Internal parts of our result are both a classification of finite groups and a classification of integral representations of a…

We investigate the representations of the symmetry groups of infinite crystals. Crystal symmetries are usually described as the finite symmetry group of a finite crystal with periodic boundary conditions, for which the Brillouin zone is a…

We give a survey of some recent results on the fusion semirings of compact quantum groups (computations of and applications to discrete quantum groups) by using the following simplifying terminology: we say that a compact quantum group G is…

A cellular algebra is called cyclic cellular if all cell modules are cyclic. Most important examples of cellular algebras appearing in representation theory are in fact cyclic cellular. We prove that if $A$ is a cyclic cellular algebra,…

We prove that the Brauer algebra, for all parameters for which it is quasi-hereditary, is Ringel dual to a category of representations of the orthosymplectic super group. As a consequence we obtain new and algebraic proofs for some results…

Let $S$ be a closed surface and $\text{Diff}_{\text{Vol}}(S)$ be the group of volume preserving diffeomorphisms of $S$. A finitely generated group $G$ is periodic of bounded exponent if there exists $k \in \mathbb{N}$ such that every…

Suppose that a finite group $G$ admits a Frobenius group of automorphisms FH of coprime order with cyclic kernel F and complement H such that the fixed point subgroup $C_G(H)$ of the complement is nilpotent of class $c$. It is proved that…

Suppose a finite group acts on a scheme X and a finite-dimensional Lie algebra g. The corresponding equivariant map algebra is the Lie algebra M of equivariant regular maps from X to g. We classify the irreducible finite-dimensional…

The purpose of this paper is to investigate the finite group which appears in the study of the Type II $\mathbf{Z}_4$-codes. To be precise, it is characterized in terms of generators and relations, and we determine the structure of the…

Let G be a graph. The (unlabeled) configuration space of n points on G is the space of all n-element subsets of G. The fundamental group of such a configuration space is called a graph braid group. We use a version of discrete Morse theory…

We describe a purely group-theoretic condition on an element g of a finite group G which implies that g has coefficient zero in every central idempotent element of the group ring RG, provided that R is a ring of prime characteristic. We use…