This is a glossary of
representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...
in
mathematics.
The term "module" is often used synonymously for a representation; for the module-theoretic terminology, see also
glossary of module theory
Module theory is the branch of mathematics in which modules are studied. This is a glossary of some terms of the subject.
See also: Glossary of linear algebra, Glossary of ring theory, Glossary of representation theory.
A
...
.
See also
Glossary of Lie groups and Lie algebras,
list of representation theory topics
This is a list of representation theory topics, by Wikipedia page. See also list of harmonic analysis topics, which is more directed towards the mathematical analysis aspects of representation theory.
See also: Glossary of representation theory
...
and
:Representation theory.
Notations: We write
. Thus, for example, a one-representation (i.e., a character) of a group ''G'' is of the form
.
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Notes
References
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* Theodor Bröcker and Tammo tom Dieck, ''Representations of compact Lie groups'', Graduate Texts in Mathematics 98, Springer-Verlag, Berlin, 1995.
*
*
*D. Gaitsgory
Geometric Representation theory, Math 267y, Fall 2005*
*
*
Claudio Procesi
Claudio Procesi (born 31 March 1941 in Rome) is an Italian mathematician, known for works in algebra and representation theory.
Career
Procesi studied at the Sapienza University of Rome, where he received his degree (Laurea) in 1963. In 1966 he ...
(2007) ''Lie Groups: an approach through invariants and representation'', Springer, .
*
*
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.
*{{citation
, last=Lusztig , first=G.
, title=Quantum deformations of certain simple modules over enveloping algebras
, journal=
Advances in Mathematics
, volume=70
, issue=2
, date=August 1988
, pages=237–249
, doi=10.1016/0001-8708(88)90056-4 , doi-access=free
External links
*https://math.stanford.edu/~bump/
Representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...
Wikipedia glossaries using description lists