Related papers: Representations of finite groups
This article is an introduction to formal languages from the point of view of combinatorial group theory. Group theoretic applications are included and language classes are defined algebraically.
This is a preliminary version of the first chapter of a book project on the character theory of finite groups of Lie type. It provides the foundations from the general theory of reductive algebraic groups over a finite field.
These notes give a short introduction to finite Coxeter groups, their classification, and some parts of their representation theory, with a focus on the infinite families. They are based on lectures delivered by the author at the…
We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for practical computation in…
The aim of this paper is to survey some aspects of mapping class groups with focus on their finite dimensional representations arising in topological quantum field theory.
Arithmetical properties of a finite group are properties of the group which are defined by its arithmetical parameters such as the order of the group, the element orders and so on. In this paper, we discuss a number of results on…
This is a survey of recent developments in combinatorics. The goal is to give a big picture of its many interactions with other areas of mathematics, such as: group theory, representation theory, commutative algebra, geometry (including…
Arithmetic groups are groups of matrices with integral entries. We shall first discuss their origin in number theory (Gauss, Minkowski) and their role in the "reduction theory of quadratic forms". Then we shall describe these groups by…
This work presents an approach towards the representation theory of the braid groups $B_n$. We focus on finite-dimensional representations over the field of Laurent series which can be obtained from representations of infinitesimal braids,…
This article contains a basic introduction to the local study of finite groups, including a brief perspective on the theory of fusion systems and $p$-local finite groups. -- Este art\'iculo contiene una introducci\'on b\'asica al estudio…
We present an accessible introduction to basic results on groups of intermediate growth.
We develop the rudiments of a finite-dimensional representation theory of groups over idempotent semifields by considering linear actions on tropical linear spaces. This can be considered a tropical representation theory, a characteristic…
These are lecture notes that arose from a representation theory course given by the first author to the remaining six authors in March 2004 within the framework of the Clay Mathematics Institute Research Academy for high school students,…
This is an introduction to the Atlas of Lie Groups and Representations software, for computing representation and structure theory of real reductive groups. The user is led through the basic commands of the software, via numerous examples.…
There could be thousands of Introductions/Surveys of representation theory, given that it is an enormous field. This is just one of them, quite personal and informal. It has an increasing level of difficulty; the first part is intended for…
This report is an account of freely representable groups, which are finite groups admitting linear representations whose only fixed point for a nonidentity element is the zero vector. The standard reference for such groups is Wolf (1967)…
We introduce a new approach to representation theory of finite groups that uses some basic algebraic geometry and allows to do all the theory without using characters. With this approach, to any finite group $G$ we associate a finite number…
Few, if any, applications of quantum technology are as widely known as the quantum simulation of quantum matter. Consequently, many interesting questions have been sparked at the intersection of condensed matter, quantum chemistry, and…
This is a largely expository paper about how groups arise or are of interest in model theory. Included are the following topics: classifying groups definable in specific structures or theories and the relation to algebraic groups, groups…
The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A…