SU(3)-invariant Heisenberg XXX chain

[Maybe_Memorie]

I'm studying the SU(3) invariant XXX chain as part of my Bachelor's thesis.

The monodromy matrix of this system can be written as a 3x3 matrix. We perform a 2x2 decomposition of it and write is as $T(\mu)=\left( \begin{array}{cc} A(\mu) & B(\mu) \\ C(\mu) & D (\mu) \end{array} \right)$

For a system to be integrable it has an R-matrix which satisfies the Yang-Baxter relation. I don't know how to decompose the R-matrix though.

Kulish/Resithiken writes it as, for the GL(N) case,
$R(\mu)=\left( \begin{array}{cccc} \mu & 0 & 0 & 0 \\ 0 & \mu I & I & 0 \\ 0 & I & \mu I & 0 \\ 0 & 0 & 0 & S(\mu) \end{array} \right)$
where I is the 2x2 identity matrix and S(u) is the SU(2) R-matrix.

The main reason this is confusing me is because when we write the Identity matrix and S(u) in the blocks we don't get the correct R-matrix, so i suspect there's a change of basis going on or something.

Any help is appreciated.

 

[Greg Bernhardt]

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?