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PreprintCC BY 4.0arXiv

A Mixed Robinson--Schensted--Knuth Construction in the Representation Theory of GLn 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 GLn(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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Cite

BibTeXRIS
BibTeX
@misc{fischer2026mixed,
  title = {{A Mixed Robinson--Schensted--Knuth Construction in the Representation Theory of $\mathrmGL_n$ over Local non-Archimedean Fields}},
  author = {Ilse Fischer and Markus Reibnegger},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.27173},
  eprint = {2608.27173},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.27173},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A Mixed Robinson--Schensted--Knuth Construction in the Representation Theory of GL_n over Local non-Archimedean Fields
AU  - Ilse Fischer
AU  - Markus Reibnegger
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2608.27173
UR  - https://arxiv.org/abs/2608.27173
AB  - We present a simple combinatorial method for computing the socle of representations of 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.
ER  -