Adjoint orbits of semisimple Lie algebras
$begingroup$
Let $mathfrak g$ be a semi-simple (complex) Lie algebra and let $G$ be a Lie group with Lie algebra $mathfrak g$. Denote by $mathcal O$ the orbit of an element $H in mathfrak h$ under the adjoint action of $G$, where $mathfrak h$ is the Cartan subalgebra of $mathfrak g$.
What is the dimension of $mathcal O$?
What else can be said about the structure of $mathcal O$?
What is a good reference?
reference-request lie-groups lie-algebras
asked Dec 2 '18 at 11:02
EarthliŋEarthliŋ
762927
$endgroup$
add a comment |
$begingroup$
Let $mathfrak g$ be a semi-simple (complex) Lie algebra and let $G$ be a Lie group with Lie algebra $mathfrak g$. Denote by $mathcal O$ the orbit of an element $H in mathfrak h$ under the adjoint action of $G$, where $mathfrak h$ is the Cartan subalgebra of $mathfrak g$.
What is the dimension of $mathcal O$?
What else can be said about the structure of $mathcal O$?
What is a good reference?
reference-request lie-groups lie-algebras
asked Dec 2 '18 at 11:02
EarthliŋEarthliŋ
762927
$endgroup$
add a comment |
$begingroup$
Let $mathfrak g$ be a semi-simple (complex) Lie algebra and let $G$ be a Lie group with Lie algebra $mathfrak g$. Denote by $mathcal O$ the orbit of an element $H in mathfrak h$ under the adjoint action of $G$, where $mathfrak h$ is the Cartan subalgebra of $mathfrak g$.
What is the dimension of $mathcal O$?
What else can be said about the structure of $mathcal O$?
What is a good reference?
reference-request lie-groups lie-algebras
asked Dec 2 '18 at 11:02
EarthliŋEarthliŋ
762927
$endgroup$
Let $mathfrak g$ be a semi-simple (complex) Lie algebra and let $G$ be a Lie group with Lie algebra $mathfrak g$. Denote by $mathcal O$ the orbit of an element $H in mathfrak h$ under the adjoint action of $G$, where $mathfrak h$ is the Cartan subalgebra of $mathfrak g$.
What is the dimension of $mathcal O$?
What else can be said about the structure of $mathcal O$?
What is a good reference?
reference-request lie-groups lie-algebras
reference-request lie-groups lie-algebras
asked Dec 2 '18 at 11:02
EarthliŋEarthliŋ
762927
asked Dec 2 '18 at 11:02
EarthliŋEarthliŋ
762927
asked Dec 2 '18 at 11:02
EarthliŋEarthliŋ
762927
asked Dec 2 '18 at 11:02
EarthliŋEarthliŋ
762927
asked Dec 2 '18 at 11:02
EarthliŋEarthliŋ
762927
762927
add a comment |
add a comment |
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