weight (Lie algebras)
where is the dual space of and
Now let be a semi-simple Lie algebra. Fix a Cartan subalgebra , then is abelian. Let be a representation whose restriction to is diagonalisable. Then for any , the space is the weight space of with respect to . The multiplicity of with respect to is the dimension of :
If the multiplicity of is greater than zero, then is called a weight of the representation .
A representation of a semi-simple Lie algebra is determined by the multiplicities of its weights.
|Title||weight (Lie algebras)|
|Date of creation||2013-03-22 13:11:42|
|Last modified on||2013-03-22 13:11:42|
|Last modified by||GrafZahl (9234)|