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

Gurevich, Maxim; Lapid, Erez

doi:10.1090/ert/578

Robinson–Schensted–Knuth correspondence in the representation theory of the general linear group over a non-archimedean local field
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by Maxim Gurevich and Erez Lapid; with an appendix by Mark Shimozono

Represent. Theory 25 (2021), 644-678

DOI: https://doi.org/10.1090/ert/578

Published electronically: July 28, 2021

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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 (DRS) 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.

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