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


Authors: Maxim Gurevich and Erez Lapid; with an appendix by Mark Shimozono
Journal: Represent. Theory 25 (2021), 644-678
MSC (2020): Primary 05E10, 22E50
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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Additional Information

Maxim Gurevich
Affiliation: Department of Mathematics, Technion – Israel Institute of Technology, Haifa, Israel
MR Author ID: 1200700
ORCID: 0000-0003-4693-0556
Email: maxg@technion.ac.il

Erez Lapid
Affiliation: Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel
MR Author ID: 631395
ORCID: 0000-0001-7204-6452
Email: erez.m.lapid@gmail.com

Mark Shimozono
MR Author ID: 361111
Email: mshimo@math.vt.edu.

Received by editor(s): June 18, 2020
Received by editor(s) in revised form: October 8, 2020, and May 4, 2021
Published electronically: July 28, 2021
Additional Notes: The first author was partially supported by the Israel Science Foundation (grant No. 737/20)
Article copyright: © Copyright 2021 American Mathematical Society