highest weight vector

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• Weight (representation theory) — In the mathematical field of representation theory, a weight of an algebra A over a field F is an algebra homomorphism from A to F, or equivalently, a one dimensional representation of A over F. It is the algebra analogue of a multiplicative… …   Wikipedia

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• Verma module — Verma modules, named after Daya Nand Verma, are objects in the representation theory of Lie algebras, a branch of mathematics. The definition of a Verma module looks complicated, but Verma modules are very natural objects, with useful properties …   Wikipedia

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• Cartan's theorem — In mathematics, there are two basic results in Lie group theory that go by the name Cartan s theorem. They are both named for Élie Cartan.:1. The theorem that for a Lie group G , any closed subgroup is a Lie subgroup.:2. A theorem on highest… …   Wikipedia