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arXiv · 1902.09180

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

Maxim Gurevich·Erez Lapid
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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.

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Maxim Gurevich, Erez Lapid. 2020-06-18. Robinson-Schensted-Knuth correspondence in the representation theory of the general linear group over a non-archimedean local field. https://doi.org/10.1090/ert%2F578

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