Theorems about algebras | Lie algebras | Representation theory
In representation theory, a branch of mathematics, the theorem of the highest weight classifies the irreducible representations of a complex semisimple Lie algebra . There is a closely related theorem classifying the irreducible representations of a connected compact Lie group . The theorem states that there is a bijection from the set of "dominant integral elements" to the set of equivalence classes of irreducible representations of or . The difference between the two results is in the precise notion of "integral" in the definition of a dominant integral element. If is simply connected, this distinction disappears. The theorem was originally proved by Élie Cartan in his 1913 paper. The version of the theorem for a compact Lie group is due to Hermann Weyl. The theorem is one of the key pieces of representation theory of semisimple Lie algebras. (Wikipedia).
Math 101 091317 Introduction to Analysis 06 Introduction to the Least Upper Bound Axiom
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From playlist Course 6: Introduction to Analysis (Fall 2017)
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From playlist Course 6: Introduction to Analysis
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From playlist Course 6: Introduction to Analysis (Fall 2017)
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Verlinde Dimension Formula for the Space of Conformal Blocks and the moduli of... - Shrawan Kumar
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