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Higher Laplacians on pseudo-Hermitian symmetric spaces

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Benjamin Schwarz

Representation Theory · Submitted 14 Oct 2014

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

The authors' main claim We show that $L_1,L_3,\ldots, L_{2r-1}$ form a set of algebraically independent generators for the algebra $\mathbb{D}_G(X)$ of $G$-invariant differential operators on $X$, where $r$ denotes the rank of $X$.

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arXiv ID1410.3807 (version 1)
Pith ID6EVIAV4A, Pith's permanent record of this paper and its review
CitationBenjamin Schwarz. "Higher Laplacians on pseudo-Hermitian symmetric spaces." arXiv:1410.3807 (2014). https://pith.science/paper/6EVIAV4A
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,764 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.28 · compares with prior results 0.75 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Let $X=G/H$ be a symmetric space for a real simple Lie group $G$, equipped with a $G$-invariant complex structure. Then, $X$ is a pseudo-Hermitian manifold, and in this geometric setting, higher Laplacians $L_m$ are defined for each positive integer $m$, which generalize the ordinary Laplace-Beltrami operator. We show that $L_1,L_3,\ldots, L_{2r-1}$ form a set of algebraically independent generators for the algebra $\mathbb{D}_G(X)$ of $G$-invariant differential operators on $X$, where $r$ denotes the rank of $X$. This confirms a conjecture of Engli\v{s} and Peetre, originally stated for the class of Hermitian symmetric spaces.

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 $X=G/H$ be a symmetric space for a real simple Lie group $G$, equipped with a $G$-invariant complex structure. background 1.00 0.08 0.02 asserted 0.96
s1 Then, $X$ is a pseudo-Hermitian manifold, and in this geometric setting, higher Laplacians $L_m$ are defined for each positive integer $m$, which generalize the ordinary Laplace-Beltrami operator. background 0.98 0.17 0.05 asserted 1.00
s2 We show that $L_1,L_3,\ldots, L_{2r-1}$ form a set of algebraically independent generators for the algebra $\mathbb{D}_G(X)$ of $G$-invariant differential operators on $X$, where $r$ denotes the rank of $X$. result 0.99 0.95 0.88 asserted 1.00
s3 This confirms a conjecture of Engli\v{s} and Peetre, originally stated for the class of Hermitian symmetric spaces. interpretation 0.89 0.33 0.18 asserted 1.00

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 $X=G/H$ be a symmetric space for a real simple Lie group $G$, equipped with a $G$-invariant complex structure. Then, $X$ is a pseudo-Hermitian manifold, and in this geometric setting, higher Laplacians $L_m$ are defined for each positive integer $m$, which generalize the ordinary Laplace-Beltrami operator. We show that $L_1,L_3,\ldots, L_{2r-1}$ form a set of algebraically independent generators for the algebra $\mathbb{D}_G(X)$ of $G$-invariant differential operators on $X$, where $r$ denotes the rank of $X$. This confirms a conjecture of Engli\v{s} and Peetre, originally stated for the class of Hermitian symmetric spaces.

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