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Results tagged with lie-algebras
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user 11056
Lie algebras are algebraic structures which were introduced to study the concept of infinitesimal transformations. The term "Lie algebra" (after Sophus Lie) was introduced by Hermann Weyl in the 1930s. In older texts, the name "infinitesimal group" is used. Related mathematical concepts include Lie groups and differentiable manifolds.
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List of irreducible representations whose weights are in a single Weyl group orbit
Let $\mathfrak g$ be a (finite dimensional) simple (nonabelian) Lie algebra
over $\mathbb C$. I need a complete list of irreducible (nontrivial) representations $V$
of $\mathfrak g$ such that the Weyl …
- 853
4
votes
2
answers
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real representation of real semi simple Lie algebra
Let $\mathfrak g$ be a real simple noncompact Lie algebra. Are there any correspondence between irreducible real representations of $\mathfrak g$ and
the highest weight correspond to some positive s …
- 853
3
votes
0
answers
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rational representation of semisimple algebraic group
Let $G$ be a connected semisimple algebraic group defined over $\mathbb Q$. Could some expert give me a complete classification of finite dimensional $\mathbb Q$-irreducible representations of $G$?
…
- 853
0
votes
1
answer
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generalization of highest weight theorem for semisimple lie algebras
Let $\mathfrak g$ be a real semisimple Lie algebra (without compact factors) with Iwasawa decomposition
$\mathfrak g=\mathfrak k\oplus \mathfrak a\oplus \mathfrak u$.
Let $\mathfrak p$ be a
para …
- 853