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arXiv · 2608.27173

A Mixed Robinson--Schensted--Knuth Construction in the Representation Theory of $\mathrm{GL}_n$ over Local non-Archimedean Fields

Ilse Fischer·Markus Reibnegger
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Abstract

We present a simple combinatorial method for computing the socle of representations of $\mathrm{GL}_n(F)$, where $F$ is a local non-Archimedean field, parabolically induced from two ladder representations satisfying a permissibility condition. We adapt recent approaches to such problems using the classical Robinson--Schensted--Knuth correspondence (RSK) and introduce a new variant of RSK that we call mixed-RSK. Some combinatorial properties of this map are investigated and then used to resolve a conjecture of Erez Lapid.

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Ilse Fischer, Markus Reibnegger. 2026-09-21. A Mixed Robinson--Schensted--Knuth Construction in the Representation Theory of $\mathrm{GL}_n$ over Local non-Archimedean Fields. https://arxiv.org/abs/2608.27173

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