classification of finite-dimensional representations of semi-simple Lie algebras
If is a semi-simple Lie algebra, then we say that an representation has highest weight , if there is a vector , the weight space of , such that for in any positive root space, and is called a highest vector, or vector of highest weight.
There is a unique (up to isomorphism) irreducible finite dimensional representation of with highest weight for any dominant weight , where is the weight lattice of , and every irreducible representation of is of this type.
|Title||classification of finite-dimensional representations of semi-simple Lie algebras|
|Date of creation||2013-03-22 13:11:40|
|Last modified on||2013-03-22 13:11:40|
|Last modified by||bwebste (988)|
|Defines||vector of highest weight|
|Defines||highest weight representation|