Definition of Subrepresentation. Meaning of Subrepresentation. Synonyms of Subrepresentation

Here you will find one or more explanations in English for the word Subrepresentation. Also in the bottom left of the page several parts of wikipedia pages related to the word Subrepresentation and, of course, Subrepresentation synonyms and on the right images related to the word Subrepresentation.

Definition of Subrepresentation

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Meaning of Subrepresentation from wikipedia

- In representation theory, a subrepresentation of a representation ( π , V ) {\displaystyle (\pi ,V)} of a group G is a representation ( π | W , W ) {\displaystyle...
- {\displaystyle A} is a nonzero representation that has no proper nontrivial subrepresentation ( ρ | W , W ) {\displaystyle (\rho |_{W},W)} , with W ⊂ V {\displaystyle...
- V is a sum of simple subrepresentations. Each subrepresentation W of V admits a complementary representation: a subrepresentation W' such that V = W ⊕...
- properties seem tautologous, it is a fundamental object of the theory. A subrepresentation is equivalent to a trivial representation, for example, if it consists...
- both the subrepresentation and the quotient have smaller dimension. There are counterexamples where a representation has a subrepresentation, but only...
- invariant under the group action is called a subrepresentation. If V has exactly two subrepresentations, namely the zero-dimensional subspace and V itself...
- if and only if every irreducible representation of G occurs as a subrepresentation of SnV (the n-th symmetric power of the representation V) for a sufficiently...
- theorem that, while the decomposition into a direct sum of irreducible subrepresentations may not be unique, the irreducible pieces have well-defined multiplicities...
- representation a subrepresentation of V. Every representation of G has itself and the zero vector space as trivial subrepresentations. A representation...
- representations. These are irreducible in the sense that the only subrepresentation is the whole space or zero. Minimally ramified representations. Modular...