Developments on the Jordan-Schwinger construction and contraction for the $su_q(2)$

The contraction and Jordan-Schwinger construction connect the $su(2)$ and the heisenberg algebra, going in oposite directions. This persists in the q-deformed cases, but in a slightly different way. This work investigates this further, discussing some details and results found in the litterature and presenting some new ones, including a non-linear expression that leads the contraction back to the original q-boson algebra used in the Jordan-Schwinger construction.

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