What does irreducible representation mean?
Definitions for irreducible representation
ir·re·duc·ible rep·re·sen·ta·tion
This dictionary definitions page includes all the possible meanings, example usage and translations of the word irreducible representation.
Wikipedia
Irreducible representation
In mathematics, specifically in the representation theory of groups and algebras, an irreducible representation ( ρ , V ) {\displaystyle (\rho ,V)} or irrep of an algebraic structure A {\displaystyle A} is a nonzero representation that has no proper nontrivial subrepresentation ( ρ | W , W ) {\displaystyle (\rho |_{W},W)} , with W ⊂ V {\displaystyle W\subset V} closed under the action of { ρ ( a ) : a ∈ A } {\displaystyle \{\rho (a):a\in A\}} . Every finite-dimensional unitary representation on a Hilbert space V {\displaystyle V} is the direct sum of irreducible representations. Irreducible representations are always indecomposable (i.e. cannot be decomposed further into a direct sum of representations), but converse may not hold, e.g. the two-dimensional representation of the real numbers acting by upper triangular unipotent matrices is indecomposable but reducible.
Numerology
Chaldean Numerology
The numerical value of irreducible representation in Chaldean Numerology is: 1
Pythagorean Numerology
The numerical value of irreducible representation in Pythagorean Numerology is: 6
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"irreducible representation." Definitions.net. STANDS4 LLC, 2024. Web. 27 Apr. 2024. <https://www.definitions.net/definition/irreducible+representation>.
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