You Qi, Joshua Sussan
We categorify tensor products of the fundamental representation of quantum $\mathfrak{sl}_2$ at prime roots of unity building upon earlier work where a tensor product of two Weyl modules was categorified.
This paper contains 48 sections, 89 theorems, 411 equations.
Theorem 1
There is an action of the derived $p$-DG category of $\dot{\mathcal{U}}$ on $\oplus_{n=0}^l \mathcal{D}^c(S_n^l)$. The action induces an identification of the Grothendieck groups where the right hand side is the tensor product of the quantum $\mathfrak{sl}_2$ Weyl module $V_1$ at a primitive $p$th root of unity.
