List questions from lie-groups

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List of simple roots in the H-basis for various Lie algebras?

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Representation of $sl(2,R)$.

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Stabilizer subgroup of adjoint action

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Elements of SO(n) is block-diagonalizable

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Solving $\lambda U^{\dagger}V -\bar{\lambda} V^{\dagger}U = A$

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How to understand the definition of Killing form?

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Algebraic groups with no small subgroups

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Automorphism group of a lie algebra as a lie subgroup of $GL(\frak g)$

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Orbit of a Weight Vector?

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How to understand that minors are matrix elements in fundamental representations of $SL_n$?

Published on 18 Jul 2015 - 2:42

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Do we have $\mathbb{C}[\text{SL}_n] = \bigoplus_{\lambda, \,\text{ht}(\lambda)\leq n} V_{\lambda} $?

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How to see that SL(2,C) is simply connected?

Published on 16 Apr 2026 - 19:29

248

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Inner Automorphism of Lie algebras in Terms of Roots and Weights?

Published on 24 Apr 2026 - 13:36

134

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Branching rules without previous knowledge of the projection matrix?

Published on 24 Apr 2026 - 13:28

List Question

Transitive Lie group actions and surjectivity of maps

List of simple roots in the H-basis for various Lie algebras?

Representation of $sl(2,R)$.

Stabilizer subgroup of adjoint action

Elements of SO(n) is block-diagonalizable

Solving $\lambda U^{\dagger}V -\bar{\lambda} V^{\dagger}U = A$

How to understand the definition of Killing form?

Algebraic groups with no small subgroups

Automorphism group of a lie algebra as a lie subgroup of $GL(\frak g)$

Orbit of a Weight Vector?

How to understand that minors are matrix elements in fundamental representations of $SL_n$?

Do we have $\mathbb{C}[\text{SL}_n] = \bigoplus_{\lambda, \,\text{ht}(\lambda)\leq n} V_{\lambda} $?

How to see that SL(2,C) is simply connected?

Inner Automorphism of Lie algebras in Terms of Roots and Weights?

Branching rules without previous knowledge of the projection matrix?

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