On Semisimplification of Tensor Categories

We develop the theory of semisimplifications tensor categories defined by Barrett and Westbury. In particular, we compute semisimplification category representations a finite group in characteristic p terms normalizer its Sylow p-subgroup. This allows us to representation symmetric Sn+p p, where 0 ≤ n − 1, Deligne $$ \underline { \mathop {\mathrm {Rep}} \nolimits }^{\mathrm {ab}}S_t$$ , t ∈ℕ. also Kac-De Concini quantum Borel subalgebra $$\mathfrak {sl}_2$$ . study functors between Verlinde semisimple algebraic groups arising from construction objects type modular (i.e., generating fusion semisimplification). Finally, determine tilting GL(n), SL(n), PGL(n) 2. appendix, classify categorifications Grothendieck ring SO(3) truncations.