Decomposing SU(4) into SU(3) x U(1)

  • #1
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2

Main Question or Discussion Point

I'm solving these problems concerning the SU(4) group and I've reached the point where I have determined the Cartan matrix of SU(4), its inverse and the weight schemes for (1 0 0) and (0 1 0) highest weight states.

83052426_998197147219953_6309952079091728384_n.jpg

How do I decompose the (1 0 0) and (0 1 0) into irreps of SU(3) x U(1) using the inverse of the Cartan matrix of SU(4) and the weight scheme?
 

Answers and Replies

  • #2
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Can you elaborate who ##SU(4)## is connected to ##SU(3) \times U(1)##? The dimension of ##SU(n)## is ##n^2-1## and the dimension of ##U(n)## is ##n^2##. Hence we have ##15## on one side and ##9## on the other.

I only know the irreducible representations of ##\mathfrak{su}(2)##, so I'm not sure what the classification theorem for ##\mathfrak{su}(4)## and ##\mathfrak{su}(3)## says. Not to mention the groups.
 

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