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

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