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We construct new "standard modules" for the representations of general lineargroups over a local non-archimedean field. The construction uses a modifiedRobinson-Schensted-Knuth correspondence for Zelevinsky's multisegments.  Typically, the new class categorifies the basis of Doubilet, Rota, and Steinfor matrix polynomial rings, indexed by bitableaux. Hence, our main resultprovides a link between the dual canonical basis (coming from quantum groups)and the DRS basis.

Robinson-Schensted-Knuth correspondence in the representation theory of the general linear group over a non-archimedean local field