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Loewy structure of $G_1T$-Verma modules of singular highest weights

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Noriyuki Abe, Masaharu Kaneda

Representation Theory · Submitted 28 Jan 2015

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

The authors' main claim We show that the $G_1T$-Verma modules of singular highest weights are all rigid, determine their Loewy length, and describe their Loewy structure using the periodic Kazhdan-Lusztig $Q$-polynomials.

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arXiv ID1501.07029 (version 2)
Pith IDW77VPA6Y, Pith's permanent record of this paper and its review
CitationMasaharu Kaneda, Noriyuki Abe. "Loewy structure of $G_1T$-Verma modules of singular highest weights." arXiv:1501.07029 (2015). https://pith.science/paper/W77VPA6Y
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,097 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.90 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.52 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Let $G$ be a reductive algebraic group over an algebraically closed field of positive characteristic, $G_1$ the Frobenius kernel of $G$, and $T$ a maximal torus of $G$. We show that the $G_1T$-Verma modules of singular highest weights are all rigid, determine their Loewy length, and describe their Loewy structure using the periodic Kazhdan-Lusztig $Q$-polynomials. We assume that the characteristic of the field is large enough that, in particular, Lusztig's conjecture for the irreducible $G_1T$-characters hold.

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 $G$ be a reductive algebraic group over an algebraically closed field of positive characteristic, $G_1$ the Frobenius kernel of $G$, and $T$ a maximal torus of $G$. background 1.00 0.05 0.02 asserted 0.78
s1 We show that the $G_1T$-Verma modules of singular highest weights are all rigid, determine their Loewy length, and describe their Loewy structure using the periodic Kazhdan-Lusztig $Q$-polynomials. result 0.56 0.96 0.95 asserted 1.00
s2 We assume that the characteristic of the field is large enough that, in particular, Lusztig's conjecture for the irreducible $G_1T$-characters hold. limitation 0.86 0.21 0.02 asserted 0.96

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

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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 $G$ be a reductive algebraic group over an algebraically closed field of positive characteristic, $G_1$ the Frobenius kernel of $G$, and $T$ a maximal torus of $G$. We show that the $G_1T$-Verma modules of singular highest weights are all rigid, determine their Loewy length, and describe their Loewy structure using the periodic Kazhdan-Lusztig $Q$-polynomials. We assume that the characteristic of the field is large enough that, in particular, Lusztig's conjecture for the irreducible $G_1T$-characters hold.

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