Glossary of representation theory explained

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 .

Notations: We write

G _{m} = GL _{1} . Thus, for example, a one-representation (i.e., a character) of a group G is of the form \chi: G \to G _{m} .

References

• • Theodor Bröcker and Tammo tom Dieck, Representations of compact Lie groups, Graduate Texts in Mathematics 98, Springer-Verlag, Berlin, 1995.
    • Web site: D. . Gaitsgory . Geometric Representation theory, Math 267y . Fall 2005 . https://web.archive.org/web/20141123183220/http://www.math.harvard.edu/~gaitsgde/267y/index.html . 23 November 2014.
• Book: Humphreys, James E.. Introduction to Lie Algebras and Representation Theory. Graduate Texts in Mathematics. 9. Springer-Verlag. New York. 1972. 978-0-387-90053-7. registration.
  • Claudio Procesi (2007) Lie Groups: an approach through invariants and representation, Springer, .
• Book: Serre , Jean-Pierre . Jean-Pierre Serre . Linear Representations of Finite Groups . registration . Graduate Texts in Mathematics, 42 . . New York–Heidelberg . 1977-09-01 . 978-0-387-90190-9 . 0450380 . 0355.20006 .
• N. Wallach, Real Reductive Groups, 2 vols., Academic Press 1988,

Further reading

• M. Duflo et M. Vergne, La formule de Plancherel des groupes de Lie semi-simples réels, in “Representations of Lie Groups;” Kyoto, Hiroshima (1986), Advanced Studies in Pure Mathematics 14, 1988.

External links

• https://math.stanford.edu/~bump/