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The indecomposable objects in the center of Deligne's category Re̲pSt$\protect\underline{{\rm Re}}\!\operatorname{p}S_t$

The indecomposable objects in the center of Deligne's category Re̲pSt$\protect\underline{{\rm Re}}\!\operatorname{p}S_t$

We classify the indecomposable objects in the monoidal center of Deligne's interpolation category $Rep(S_t)$ by viewing $Rep(S_t)$ as a model-theoretic limit in rank and characteristic. We further prove that the center of $Rep(S_t)$ is semisimple if and only if $t$ is not a non-negative integer. In addition, we identify the …