Representation theory studies how algebraic structures "act" on objects. A simple example is the way a polygon is transformed by its symmetries under reflections and rotations, which are all …

Introduction Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory …

Representation theory is the study of groups through the lens of linear algebra, allowing us to observe how a group acts on a vector space while making use of all the standard theorems …

May 20, 2016 · If V is a representation of Cn, there is a basis of V for which the action of every element of Cn is a diagonal matrix, with the n-th roots of 1 on the diagonal.

Representation theory is simple to define: it is the study of the ways in which a given group may act on vector spaces. It is almost certainly unique, however, among such clearly delineated …

Representation theory is fundamental in the study of objects with symmetry. It arises in contexts as diverse as card shuffling and quantum mechanics.

From this point of view, geometry asks, “Given a geometric object X, what is its group of symmetries?” Representation theory reverses the question to “Given a group G, what objects …

This section provides the lecture notes from the course. The present lecture notes arose from a representation theory course given by Prof. Etingof in March 2004 within the framework of the …

May 7, 2025 · Representation theory is incredibly useful, as once something is being represented by matrices, it allows us to apply well-known and widely-used techniques from linear algebra.

Representation theory is a very broad subject. In a nutshell, it is a systematic study of how abstract groups (or algebras) can be represented by concrete linear transformations of a …