Steadied Khovanov-Lauda-Rouquier algebras and local models for blocks

It's known that many different blocks of FₚSₙ for different values of n are equivalent as categories, though the corresponding block algebras are almost never isomorphic. Thus, it is a challenging problem to give one particularly nice representative of this Morita equivalence class of algebras. This has been accomplished for the case of RoCK blocks through work of Chuang--Kessar, Turner, and Evseev--Kleshchev. In this paper, we give a new perspective on this problem, applying not just to RoCK blocks of Sₙ, but also to all blocks of Ariki--Koike algebras. We do this by considering steadied quotients of KLRW algebras: these algebras are a natural generalization of cyclotomic quotients, already related to Sₙ and Ariki--Koike algebras in work of Brundan--Kleshchev. These algebras are defined by ``tilting'' the cyclotomic relations so that we kill the two-sided ideal defined by certain configurations on the left and right sides of our diagrams. We show a Morita equivalence between these algebras and blocks of Ariki-Koike algebras generalizing the work discussed above.