Question

Show that any representation of $\mathfrak{sl}(2,\mathbb C)$ is a subrepresentation of $V^{\otimes m} \oplus V^{\otimes {(m+1)}}$ for some $m$

score 112 · Answer 1 · 2026-04-13 18:40:39

Show that any representation of $\mathfrak{sl}(2,\mathbb C)$ is a subrepresentation of $V^{\otimes m} \oplus V^{\otimes {(m+1)}}$ for some $m$

score 88 · Answer 2 · 2026-04-17 07:29:48

88

Views

Lie subalgebra generated by a subset of a basis of root system

Published on 17 Apr 2026 - 7:29

score 320 · Answer 3 · 2026-03-29 07:19:38

320

Views

Compute $ad_X$, $ad_Y$, and $ad_Z$ relative to a basis

Published on 29 Mar 2026 - 7:19

score 47 · Answer 4 · 2026-04-15 10:48:05

47

Views

Adjoint matrix in $\mathbb{so_3}$

Published on 15 Apr 2026 - 10:48

score 584 · Answer 5 · 2026-04-15 23:24:07

584

Views

The Lie algebra of the generalized unitary group $\{g \in GL_n(\mathbb{C}) : gS\bar{g}^t=S\}$ is $\{XS+S\overline{X}{}^t=0\}$

Published on 15 Apr 2026 - 23:24

score 30 · Answer 6 · 2026-04-13 23:03:41

30

Views

Parabolic subalgeba

Published on 13 Apr 2026 - 23:03

score 101 · Answer 7 · 2026-04-16 04:00:25

101

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Lie algebra associated to Leibniz algebra

Published on 16 Apr 2026 - 4:00

score 52 · Answer 8 · 2026-04-15 05:57:04

52

Views

Ad-nilpotency is preserved under conjugation

Published on 15 Apr 2026 - 5:57

score 193 · Answer 9 · 2016-04-11 10:59:10

193

Views

Finite dimensional, irreducible representations of the Lie superalgebra gl(1|1)

Published on 11 Apr 2016 - 10:59

score 511 · Answer 10 · 2026-04-16 10:10:34

511

Views

Why can we find a basis for the elements of the Lie algebra?

Published on 16 Apr 2026 - 10:10

score 504 · Answer 11 · 2026-03-26 01:12:38

504

Views

Let $G$ be a Lie group and $H$ be a closed subgroup of $G$. Show that if $H$ and homogeneous space $\frac{G}{H}$ are connected, then $G$ is connected.

Published on 26 Mar 2026 - 1:12

score 228 · Answer 12 · 2026-04-16 03:48:53

228

Views

Compute the associated induced Lie algebra action $\text{d}\pi$

Published on 16 Apr 2026 - 3:48

score 291 · Answer 13 · 2026-04-07 17:27:59

291

Views

Is every element contained in a Borel subalgebra?

Published on 07 Apr 2026 - 17:27

score 51 · Answer 14 · 2026-04-16 21:01:32

51

Views

Show that $\left.\dfrac{d}{d s}\right|_{s=0}X_\eta (m)(f\circ \varphi_{\exp(s\xi )})=(X_\eta f)_{*,m}(X_\xi (m))$

Published on 16 Apr 2026 - 21:01

score 524 · Answer 15 · 2026-04-12 04:03:22

524

Views

Do I understand the Chevalley Restriction Theorem correctly?

Published on 12 Apr 2026 - 4:03

List Question

Show that any representation of $\mathfrak{sl}(2,\mathbb C)$ is a subrepresentation of $V^{\otimes m} \oplus V^{\otimes {(m+1)}}$ for some $m$

Lie subalgebra generated by a subset of a basis of root system

Compute $ad_X$, $ad_Y$, and $ad_Z$ relative to a basis

Adjoint matrix in $\mathbb{so_3}$

The Lie algebra of the generalized unitary group $\{g \in GL_n(\mathbb{C}) : gS\bar{g}^t=S\}$ is $\{XS+S\overline{X}{}^t=0\}$

Parabolic subalgeba

Lie algebra associated to Leibniz algebra

Ad-nilpotency is preserved under conjugation

Finite dimensional, irreducible representations of the Lie superalgebra gl(1|1)

Why can we find a basis for the elements of the Lie algebra?

Let $G$ be a Lie group and $H$ be a closed subgroup of $G$. Show that if $H$ and homogeneous space $\frac{G}{H}$ are connected, then $G$ is connected.

Compute the associated induced Lie algebra action $\text{d}\pi$

Is every element contained in a Borel subalgebra?

Show that $\left.\dfrac{d}{d s}\right|_{s=0}X_\eta (m)(f\circ \varphi_{\exp(s\xi )})=(X_\eta f)_{*,m}(X_\xi (m))$

Do I understand the Chevalley Restriction Theorem correctly?

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