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Canonical filtrations on Harish-Chandra modules

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Ivan Losev

Representation Theory · Submitted 21 Sep 2023

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

The authors' main claim The goal of this paper is to show that a wide class of Harish-Chandra $(\mathfrak{g},K)$-modules including all irreducible ones come with a certain canonical filtration.

how it is stated · asserted 1.00 read the record →

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arXiv ID2309.12007 (version 1)
Pith IDW2ILMGPD, Pith's permanent record of this paper and its review
CitationIvan Losev. "Canonical filtrations on Harish-Chandra modules." arXiv:2309.12007 (2023). https://pith.science/paper/W2ILMGPD
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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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 1,636 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.11 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.05 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

The goal of this paper is to show that a wide class of Harish-Chandra $(\mathfrak{g},K)$-modules including all irreducible ones come with a certain canonical filtration.

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 The goal of this paper is to show that a wide class of Harish-Chandra $(\mathfrak{g},K)$-modules including all irreducible ones come with a certain canonical filtration. contribution 0.81 0.75 0.72 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 v1
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

The goal of this paper is to show that a wide class of Harish-Chandra $(\mathfrak{g},K)$-modules including all irreducible ones come with a certain canonical filtration.

Human review

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What this paper does with the arXiv papers it cites

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 5 sentences without a confident label

Uses the method or tool of 1 paper
Compares with 1 paper
Cites as support 1 paper
  • One can show, [ref] , that $M_ħ^∧_χ$ decomposes as $[[L,ħ]]⊗_[[ħ]]N'_ħ$, where $L$ is the $-1$-eigenspace for $θ$ in $T_χGχ$, a lagrangian subspace, and $N'_ħ$ is the annihilator of the Lie algebra action of $L$ on $M_ħ^∧_χ$.

    On Harish-Chandra modules over quantizations of nilpotent orbits · Construction and properties · 0.97

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