Search results
Results from the WOW.Com Content Network
For n = 3 the obvious analogue of the (n − 1)-dimensional representation is reducible – the permutation representation coincides with the regular representation, and thus breaks up into the three one-dimensional representations, as A 3 ≅ C 3 is abelian; see the discrete Fourier transform for representation theory of cyclic groups.
Ammonia is an inorganic chemical compound of nitrogen and hydrogen with the formula N H 3.A stable binary hydride and the simplest pnictogen hydride, ammonia is a colourless gas with a distinctive pungent smell.
The irreducible complex characters of a finite group form a character table which encodes much useful information about the group G in a concise form. Each row is labelled by an irreducible character and the entries in the row are the values of that character on any representative of the respective conjugacy class of G (because characters are class functions).
Let V be a representation of a group G; or more generally, let V be a vector space with a set of linear endomorphisms acting on it. In general, a vector space acted on by a set of linear endomorphisms is said to be simple (or irreducible) if the only invariant subspaces for those operators are zero and the vector space itself; a semisimple representation then is a direct sum of simple ...
In more mathematical terms, the CG coefficients are used in representation theory, particularly of compact Lie groups, to perform the explicit direct sum decomposition of the tensor product of two irreducible representations (i.e., a reducible representation into irreducible representations, in cases where the numbers and types of irreducible ...
If has exactly two subrepresentations, namely the trivial subspace {0} and itself, then the representation is said to be irreducible; if has a proper nontrivial subrepresentation, the representation is said to be reducible. [19] The definition of an irreducible representation implies Schur's lemma: an equivariant map : (,) (′, ′) between ...
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
A reducible representation is one where a change of basis can be applied to bring all the matrices into block diagonal form. A representation is irreducible (irrep) if no such transformation exists. For each value of j , the 2 j +1 kets form a basis for an irreducible representation (irrep) of SO(3)/SU(2) over the complex numbers.