Related papers: Brauer's 14th Problem and Dyson's Tenfold Way

In this paper, we develop the theory of Baer invariants for triples of groups. First, we focus on the general properties of the Baer invariant of triples. Second, we prove that the Baer invariant of a triple preserves direct limits of…

Given a hyper loop algebra over a non-algebraically closed field, we address multiplicity problems in the underlying abelian tensor category of finite-dimensional representations. Namely, we give formulas for the l-characters of the simple…

This paper reviews recent results and open problems on the conductor of finite group characters, highlighting their connections to one another and to broader topics in the representation theory of finite groups.

Hypercubic groups in any dimension are defined and their conjugate classifications and representation theories are derived. Double group and spinor representation are introduced. A detailed calculation is carried out on the structures of…

In this paper, we consider representations of integers as sums of at most four distinct $m$-gonal numbers (allowing a fixed number of repeats of each polygonal number occurring in the sum). We show that the number of such representations…

We prove Clifford theoretic results on the representations of finite groups which only hold in characteristic $2$. Let $G$ be a finite group, let $N$ be a normal subgroup of $G$ and let $\varphi$ be an irreducible $2$-Brauer character of…

We first review some topics in the classical computational geometry of lines, in particular the O(n^{3+\epsilon}) bounds for the combinatorial complexity of the set of lines in R^3 interacting with $n$ objects of fixed description…

For every positive integer h, the representation function of order h associated to a subset A of the integers or, more generally, of any group or semigroup X, counts the number of ways an element of X can be written as the sum (or product,…

We present a strong upper bound on the number k(B) of irreducible characters of a p-block B of a finite group G in terms of local invariants. More precisely, the bound depends on a chosen major B-subsection (u,b), its normalizer N_G(\langle…

We initiate the representation theory of the degenerate affine periplectic Brauer algebra on $n$ strands by constructing its finite-dimensional calibrated representations when $n=2$. We show that any such representation that is…

We describe a practical algorithm for computing Brauer-Manin obstructions to the existence of rational points on hyperelliptic curves defined over number fields. This offers advantages over descent based methods in that its correctness does…

We investigate two types of boundedness criteria for bilinear Fourier multiplier operators with symbols with bounded partial derivatives of all (or sufficiently many) orders. Theorems of the first type explicitly prescribe only a certain…

We describe two methods for computing $p$-modular Brauer character tables for groups of Lie type $G(p^f)$ in defining characteristic $p$, assuming that the ordinary character table of $G(p^f)$ is known, and the weight multiplicities of the…

The problem of representing a given positive integer as a sum of four squares of integers has been widely concerned for a long time, and for a given positive odd $n$ one can find a representation by doing arithmetic in a maximal order of…

The class in the Brauer group of a quaternion algebra over a field is 2-torsion. We study the following question: Which 2-torsion elements of the Brauer group of a complex function field are representable by quaternion algebras? Using…

For the first time we represent every finite group in the form of a graph in this book. The authors choose to call these graphs as identity graph, since the main role in obtaining the graph is played by the identity element of the group.…

Using the construction by Bencs and T\'{o}th of invariant random subgroups on weakly branch groups acting on regular rooted trees we produce uncountably many indecomposable characters on these groups. In fact, we study three types of…

We prove that finite groups have the same complex character tables iff the group algebras are twisted forms of each other as Drinfel'd quasi-bialgebras or iff there is non-associative bi-Galois algebra over these groups. The interpretations…

The centralizer algebra of the action of the unitary group on the real tensor powers of its natural module, is described by means of a modification in the multiplication of the signed Brauer algebras. The relationships of this algebra with…

A new presentation of the $n$-string braid group $B_n$ is studied. Using it, a new solution to the word problem in $B_n$ is obtained which retains most of the desirable features of the Garside-Thurston solution, and at the same time makes…