# weight lattice

The weight lattice^{} ${\mathrm{\Lambda}}_{W}$ of a root system^{} $R\subset E$ is the lattice

$${\mathrm{\Lambda}}_{W}=\left\{e\in E\right|\frac{(e,\alpha )}{(\alpha ,\alpha )}\in \mathbb{Z}\text{for all}r\in R\}.$$ |

Weights which lie in the weight lattice are called . If $R\subset \U0001d525$ is the root system of a semi-simple Lie algebra $\U0001d524$ with Cartan subalgebra^{} $\U0001d525$, then ${\mathrm{\Lambda}}_{W}$ is exactly the set of weights appearing in finite dimensional representations of $\U0001d524$.

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 |