weight lattice

The weight latticeMathworldPlanetmath ΛW of a root systemMathworldPlanetmath RE is the lattice

ΛW={eE|(e,α)(α,α) for all rR}.

Weights which lie in the weight lattice are called . If R𝔥 is the root system of a semi-simple Lie algebra 𝔤 with Cartan subalgebraMathworldPlanetmath 𝔥, then ΛW is exactly the set of weights appearing in finite dimensional representations of 𝔤.

Title weight lattice
Canonical name WeightLattice
Date of creation 2013-03-22 13:11:57
Last modified on 2013-03-22 13:11:57
Owner bwebste (988)
Last modified by bwebste (988)
Numerical id 9
Author bwebste (988)
Entry type Definition
Classification msc 17B20
Defines integral weight