Glossary of representation theory

This is a glossary of representation theory in mathematics.

The term "module" is often used synonymously for a representation; for the module-theoretic terminology, see also glossary of module theory.

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

Notations: We write ${\displaystyle \mathbb {G} _{m}=GL_{1}}$. Thus, for example, a one-representation (i.e., a character) of a group G is of the form ${\displaystyle \chi :G\to \mathbb {G} _{m}}$.