Simple modules for quiver Hecke algebras and the Robinson–Schensted–Knuth correspondence

We formalize some known categorical equivalences to give a rigorous treatment of smooth representations p-adic general linear groups, as ungraded modules over quiver Hecke algebras type A. Graded variants RSK-standard are constructed for algebras. Exporting recent results from the setting, we describe an effective method construction and classification all simple quotients induced maximal homogenous data. It is established that products involved in RSK fit Kashiwara-Kim notion normal sequences real modules. deduce have heads, devise formula shift grading between self-dual modules, establish properties their decomposition matrix, thus confirming expectations groups raised work author with Lapid. Subsequent will exhibit how presently introduced generalizes much-studied Specht construction, when inflated cyclotomic quotient