Glossary of representation theory

See also Glossary of Lie groups and Lie algebras, list of representation theory topics and Category:Representation theory.

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 breadth of its interest to mathematicians.

This is not surprising: group actions are ubiquitous in 20th century mathematics, and where the object on which a group acts is not a vector space, we have learned to replace it by one that is (e.g., a cohomology group, tangent space, etc.).

As a consequence, many mathematicians other than specialists in the field (or even those who think they might want to be) come in contact with the subject in various ways.