In algebra, a Weyl module is a
representation
Representation may refer to:
Law and politics
*Representation (politics), political activities undertaken by elected representatives, as well as other theories
** Representative democracy, type of democracy in which elected officials represent a ...
of a
reductive algebraic group
In mathematics, an algebraic group is an algebraic variety endowed with a group structure which is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs both to algebraic geometry and group theory.
...
, introduced by and named after
Hermann Weyl
Hermann Klaus Hugo Weyl, (; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is ass ...
. In
characteristic 0 these representations are
irreducible, but in positive characteristic they can be reducible, and their decomposition into irreducible components can be hard to determine.
See also
*
Borel–Weil–Bott theorem
*
Garnir relations
Further reading
*
*
*{{eom, id=Weyl_module, first=R., last= Dipper
Representation theory
Algebraic groups