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

Abstract

AbstractWe classify the indecomposable objects in the monoidal center of Deligne's interpolation category by viewing as a model‐theoretic limit in rank and characteristic. We further prove that the center of is semisimple if and only if is not a non‐negative integer. In addition, we identify the associated graded Grothendieck ring of this monoidal center with that of the graded sum of the centers of representation categories of finite symmetric groups with an induction product. We prove analogous statements for the abelian envelope.