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 linear …

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 and …

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 and tools that …

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 X does it act on?” …

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 subjects, in the …

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

Jan 7, 2009 · The notes cover a number of standard topics in representation theory of groups, Lie algebras, and quivers, and contain many problems and exercises.

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 seeks to understand all the possible ways that an abstract collection of symmetries can arise. Nineteenth-century representation theory helped to explain the structure of …

Representation theory is a subfield of mathematics which uses linear algebra to study algebraic objects. Representations are ubiquitous in mathematics and beyond! The Langlands program, one of the …