nLab
reducible representation
Context
Representation theory
representation theory
geometric representation theory
Ingredients
representation, 2-representation, ∞-representation
-
group, ∞-group
-
group algebra, algebraic group, Lie algebra
-
vector space, n-vector space
-
affine space, symplectic vector space
-
action, ∞-action
-
module, equivariant object
-
bimodule, Morita equivalence
-
induced representation, Frobenius reciprocity
-
Hilbert space, Banach space, Fourier transform, functional analysis
-
orbit, coadjoint orbit, Killing form
-
unitary representation
-
geometric quantization, coherent state
-
socle, quiver
-
module algebra, comodule algebra, Hopf action, measuring
Geometric representation theory
-
D-module, perverse sheaf,
-
Grothendieck group, lambda-ring, symmetric function, formal group
-
principal bundle, torsor, vector bundle, Atiyah Lie algebroid
-
geometric function theory, groupoidification
-
Eilenberg-Moore category, algebra over an operad, actegory, crossed module
-
reconstruction theorems
Contents
Definition
A representation is called:
-
reducible if it is not irreducible, hence if it contains a non-zero subrepresentation;
-
completely reducible if it is a direct sum of irreducible representations.
Last revised on July 29, 2026 at 15:29:17.
See the history of this page for a list of all contributions to it.