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

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Abstract

We construct new "standard modules" for the representations of general linear groups over a local non-archimedean field. The construction uses a modified Robinson-Schensted-Knuth correspondence for Zelevinsky's multisegments.
Typically, the new class categorifies the basis of Doubilet, Rota, and Stein for matrix polynomial rings, indexed by bitableaux. Hence, our main result provides a link between the dual canonical basis (coming from quantum groups) and the DRS basis.
Original languageEnglish
Pages (from-to)644-678
Number of pages35
JournalRepresentation Theory
Volume25
Issue number22
DOIs
StatePublished - 28 Jul 2021

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

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