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Irreducibility criterion for representations induced by essentially unitary ones (case of non-archimedean GL(n,A)

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Marko Tadic

Representation Theory · Submitted 20 Dec 2012

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We give an explicit necessary and sufficient condition for the parabolically induced representation Ind(\phi\pi) of GL(n,A) to be irreducible.

how it is stated · asserted 1.00 read the record →

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arXiv ID1212.5302 (version 2)
Pith ID5KFZUNQI, Pith's permanent record of this paper and its review
CitationMarko Tadic. "Irreducibility criterion for representations induced by essentially unitary ones (case of non-archimedean GL(n,A)." arXiv:1212.5302 (2012). https://pith.science/paper/5KFZUNQI
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,540 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.19 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.04 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

Let A be a finite dimensional central division algebra over a local non-archimedean field F. Fix any parabolic subgroup P of GL(n,A) and a Levi factor M of P. Let \pi be an irreducible unitary representation of M and \phi (not necessarily unitary) character of M. We give an explicit necessary and sufficient condition for the parabolically induced representation Ind(\phi\pi) of GL(n,A) to be irreducible.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Let A be a finite dimensional central division algebra over a local non-archimedean field F. background 1.00 0.06 0.01 asserted 0.94
s1 Fix any parabolic subgroup P of GL(n,A) and a Levi factor M of P. background 0.93 0.35 0.02 unclear 0.67
s2 Let \pi be an irreducible unitary representation of M and \phi (not necessarily unitary) character of M. background 0.96 0.11 0.03 unclear 0.57
s3 We give an explicit necessary and sufficient condition for the parabolically induced representation Ind(\phi\pi) of GL(n,A) to be irreducible. result 0.71 0.96 0.95 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Let A be a finite dimensional central division algebra over a local non-archimedean field F. Fix any parabolic subgroup P of GL(n,A) and a Levi factor M of P. Let \pi be an irreducible unitary representation of M and \phi (not necessarily unitary) character of M. We give an explicit necessary and sufficient condition for the parabolically induced representation Ind(\phi\pi) of GL(n,A) to be irreducible.

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