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Jul
15
comment Representation of $sl(2,R)$.
Sort of. The complaint is that I have some calculations involving the orbit of the action of $G=SL(2,\mathbb{R})$ on (a) the highest weight vector or (b) some vector fixed by the max. cpt. subgroup $K=SO(2)$ but I also would like to work at the Lie algebra level.
Jul
15
comment Representation of $sl(2,R)$.
@Aaron I understand that one cannot multiply a $2 \times 2$ matrix by an $n \times n$ matrix. I was just hoping something similar exists.
Jul
15
asked Representation of $sl(2,R)$.
May
4
awarded  Popular Question
Apr
27
awarded  Nice Question
Apr
21
accepted Weights in $\mathfrak{sl}(3,\mathbb{C})$
Apr
19
comment Weights in $\mathfrak{sl}(3,\mathbb{C})$
Isn't the killing form $(A,B) \mapsto tr(ad(A) ad(B))$?
Apr
19
asked Weights in $\mathfrak{sl}(3,\mathbb{C})$
Apr
19
awarded  Popular Question
Mar
26
answered The only dense linear subspace of $\mathbb{C}^n$.
Mar
20
accepted Closedness of set in product topology
Mar
20
asked Closedness of set in product topology
Mar
15
accepted support of function in topological group
Mar
13
asked support of function in topological group
Feb
21
accepted Representations of the Lie algebra $\mathfrak{sl}(2,\mathbb{C})$
Feb
21
comment Representations of the Lie algebra $\mathfrak{sl}(2,\mathbb{C})$
I don't see why. If $V_\lambda=0$, then keeping it in the sum or not has no effect. How does one get an invariant subspace if the string is broken? I'm not saying you're lying, I'm just confused.
Feb
21
asked Representations of the Lie algebra $\mathfrak{sl}(2,\mathbb{C})$
Feb
6
accepted Weyl algebra confusion
Feb
6
comment Weyl algebra confusion
Perfect. Thanks. I was being obtuse.
Feb
5
revised Weyl algebra confusion
added 2 characters in body