In algebra, a Weyl module is a
representation 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.
Ma ...
, introduced by and named after
Hermann Weyl. In
characteristic 0 these representations are
irreducible
In philosophy, systems theory, science, and art, emergence occurs when an entity is observed to have properties its parts do not have on their own, properties or behaviors that emerge only when the parts interact in a wider whole.
Emergence ...
, but in positive characteristic they can be reducible, and their decomposition into irreducible components can be hard to determine.
See also
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Borel–Weil–Bott theorem
In mathematics, the Borel–Weil–Bott theorem is a basic result in the representation theory of Lie groups, showing how a family of representations can be obtained from holomorphic sections of certain complex vector bundles, and, more generally, ...
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Garnir relations In mathematics, the Garnir relations give a way of expressing a basis of the Specht modules ''V''λ in terms of standard polytabloids.
Specht modules in terms of polytabloids
Given a partition ''λ'' of ''n'', one has the Specht module ''V''λ. In ...
Further reading
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*{{eom, id=Weyl_module, first=R., last= Dipper
Representation theory
Algebraic groups