A Mixed Robinson--Schensted--Knuth Construction in the Representation Theory of $\mathrm{GL}_n$ over Local non-Archimedean Fields
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Fischer, Ilse, Reibnegger, Markus
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Austrian Science Fund
Award: G8590477180
OpenAlex ID: W7204593253