Related papers: Brauer's 14th Problem and Dyson's Tenfold Way
We construct a finite subgroup of Brauer-Manin obstruction for detecting the existence of integral points on integral models of homogeneous spaces of linear algebraic groups of multiplicative type. As application, the strong approximation…
We develop quaternionic analysis using as a guiding principle representation theory of various real forms of the conformal group. We first review the Cauchy-Fueter and Poisson formulas and explain their representation theoretic meaning. The…
We study the problem of realising modular invariants by braided subfactors and the related problem of classifying nimreps. We develop the fusion rule structure of these modular invariants. This structure is useful tool in the analysis of…
We study tensor powers of representations of finite monoids, focusing on the growth behavior of their composition length and the number of indecomposable summands. Special attention is given to diagram monoids such as the Temperley-Lieb,…
We describe an easy way how to find supercharacter theories for a finite group, if its character table is known. Namely, we show how an arbitrary partition of the conjugacy classes or of the irreducible characters can be refined to the…
Several recent problems in the representation theory of finite groups require determining whether certain characters of almost simple groups belong to the principal block. Since the values of these characters are not yet known, we employ…
We propose the method for obtaining invariants of arbitrary representations of Lie groups that reduces this problem to known problems of linear algebra. The basis of this method is the idea of a special extension of the representation…
In this paper, we will interest in finding the number of zeros of the quadratic forms over finite fields. We will apply the tool for finding the number of rational points of supersingular curves in [6]. We will give some more tools for…
This is the first in a series of papers in which we study representations of the Brauer category and its allies. We define a general notion of triangular category that abstracts key properties of the triangular decomposition of a semisimple…
Introduction 1. The two-eigenvalue problem 2. Hecke algebra representations of braid groups 3. Duality of Jones-Wenzl representations 4. Closed images of Jones-Wenzl sectors 5. Distribution of evaluations of Jones polynomials 6. Fibonacci…
For an affine double plane defined by an equation of the form z^2 = f, we study the divisor class group and the Brauer group. Two cases are considered. In the first case, f is a product of n linear forms in k[x,y] and X is birational to a…
We give a full classification of Lie algebras of specific type in complexified Clifford algebras. These sixteen Lie algebras are direct sums of subspaces of quaternion types. We obtain isomorphisms between these Lie algebras and classical…
A real representation theory of real Clifford algebra has been studied in further detail, especially in connection with Fierz identities. As its application, we have constructed real octonion algebras as well as related octonionic triple…
We describe a method to compute the Brauer-Manin obstruction for smooth cubic surfaces over $\bbQ$ such that $\Br(S)/\Br(\bbQ)$ is of order two or four. This covers the vast majority of the cases when this group is non-zero. Our approach is…
Let $q$ be a power of a prime $p$, $G$ be a finite abelian group, where $p$ does not divide $|G|$,and let $n$ be a positive integer. In this paper we find a formula for the number of irreducible representations of $G$ of a given dimension…
The key to membrane theory is to enlarge the diffeomorphism group until 4D gravity becomes almost topological. Just one ghost survives and its central charges can cancel against matter. A simple bosonic membrane emerges, but its flat D = 28…
Let $G$ be a finite group, let $N$ be a normal subgroup of $G$ and let $\theta$ be an irreducible character of $N$. We count the real irreducible characters of $G$ lying over $\theta$
A new application of polytope theory to Lie theory is presented. Exponential sums of convex lattice polytopes are applied to the characters of irreducible representations of simple Lie algebras. The Brion formula is used to write a polytope…
In this short note we observe that the recent examples of derived-equivalent Calabi-Yau 3-folds with different fundamental groups also have different Brauer groups, using a little topological K-theory.
If G is a finite group and H is a subgroup of G, we characterize when restriction of Brauer characters from G to H is injective.