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I just want to consider the simplest case:

Let S=[0,0,0,0,1], how to derive the general formula for $Sym^k$ S?

My conjectured formula based on the results of LiE program for finite k values is:

$Sym^k(S)=\overset{\left[k/2\right]}{\underset{i=0}{\oplus}}[i,0,0,0,k-2i]$

But I have no clue how to prove it or even a derivation for the simplest case when k=2.

Any reference or tips would be greatly appreciated.

I just want to consider the simplest case:

Let S=[0,0,0,0,1], how to derive the general formula for $Sym^k$ S?

My conjectured formula based on the results of LiE program for finite k values is:

$Sym^k(S)=\overset{\left[k/2\right]}{\underset{i=0}{\oplus}}[i,0,0,0,k-2i]$

But I have no clue how to prove it or even a derivation for the simplest case when k=2.

Any reference or tips would be greatly appreciated.

PS. Sorry for confusion. Now I changed the spinor representation "V" to "S".

I just want to consider the simplest case:

Let V=[0,0,0,0,1], how to derive the general formula for $Sym^k$ V?

My conjectured formula based on the results of LiE program for finite k values is:

$Sym^k(V)=\overset{\left[k/2\right]}{\underset{i=0}{\oplus}}[i,0,0,0,k-2i]$

But I have no clue how to prove it or even a derivation for the simplest case when k=2.

Any reference or tips would be greatly appreciated.

I just want to consider the simplest case:

Let S=[0,0,0,0,1], how to derive the general formula for $Sym^k$ S?

My conjectured formula based on the results of LiE program for finite k values is:

$Sym^k(S)=\overset{\left[k/2\right]}{\underset{i=0}{\oplus}}[i,0,0,0,k-2i]$

But I have no clue how to prove it or even a derivation for the simplest case when k=2.

Any reference or tips would be greatly appreciated.