Complementary Representation

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 :Representation theory.

Notations: We write $\mathbb_m = GL_1$. Thus, for example, a one-representation (i.e., a character) of a group ''G'' is of the form $\chi: G \to \mathbb_m$.

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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.
*
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*D. Gaitsgory
Geometric Representation theory, Math 267y, Fall 2005
*
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* Claudio Procesi (2007) ''Lie Groups: an approach through invariants and representation'', Springer, .
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* 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

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