This is a glossary of
representation theory
Representation theory is a branch of mathematics that studies abstract algebra, abstract algebraic structures by ''representing'' their element (set theory), elements as linear transformations of vector spaces, and studies Module (mathematics), ...
in
mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
.
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 module (mathematics), 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 the ...
.
See also
Glossary of Lie groups and Lie algebras,
list of representation theory topics 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
*
* Theodor Bröcker and Tammo tom Dieck, ''Representations of compact
Lie group
In mathematics, a Lie group (pronounced ) is a group (mathematics), group that is also a differentiable manifold, such that group multiplication and taking inverses are both differentiable.
A manifold is a space that locally resembles Eucli ...
s'', Graduate Texts in Mathematics 98, Springer-Verlag, Berlin, 1995.
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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
''Advances in Mathematics'' is a peer-reviewed scientific journal covering research on pure mathematics. It was established in 1961 by Gian-Carlo Rota. The journal publishes 18 issues each year, in three volumes.
At the origin, the journal aimed ...
, 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 algebra, abstract algebraic structures by ''representing'' their element (set theory), elements as linear transformations of vector spaces, and studies Module (mathematics), ...
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