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Finite type multiple flag varieties of exceptional groups

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Dan Barbasch, Sergio Da Silva, Balázs Elek, Gautam Gopal Krishnan

Representation Theory · Submitted 21 Aug 2017

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

The authors' main claim We then use this method to give a complete classification for when $G$ is of type $F_4$.

how it is stated · asserted 1.00 read the record →

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arXiv ID1708.06341 (version 1)
Pith IDZS5VQKEI, Pith's permanent record of this paper and its review
CitationBal\'azs Elek, Dan Barbasch, Gautam Gopal Krishnan, Sergio Da Silva. "Finite type multiple flag varieties of exceptional groups." arXiv:1708.06341 (2017). https://pith.science/paper/ZS5VQKEI
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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, 3,569 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.94 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.06 · mentions code or data availability 0.03.

The abstract, sentence by sentence

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

Consider a simple complex Lie group $G$ acting diagonally on a triple flag variety $G/P_1\times G/P_2\times G/P_3$, where $P_i$ is parabolic subgroup of $G$. We provide an algorithm for systematically checking when this action has finitely many orbits. We then use this method to give a complete classification for when $G$ is of type $F_4$. The $E_6, E_7,$ and $E_8$ cases will be treated in a subsequent paper.

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 Consider a simple complex Lie group $G$ acting diagonally on a triple flag variety $G/P_1\times G/P_2\times G/P_3$, where $P_i$ is parabolic subgroup of $G$. background 0.99 0.13 0.03 asserted 0.60
s1 We provide an algorithm for systematically checking when this action has finitely many orbits. method 0.73 0.95 0.21 asserted 1.00
s2 We then use this method to give a complete classification for when $G$ is of type $F_4$. result 0.76 0.96 0.68 asserted 1.00
s3 The $E_6, E_7,$ and $E_8$ cases will be treated in a subsequent paper. future work 0.99 0.21 0.03 asserted 0.98

What kind of paper the classifier reports this is: method or tool 0.75 · evidence from proof or derivation 0.98.

What was examined, and what was not

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  • references and citing sentences
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  • 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

Consider a simple complex Lie group $G$ acting diagonally on a triple flag variety $G/P_1\times G/P_2\times G/P_3$, where $P_i$ is parabolic subgroup of $G$. We provide an algorithm for systematically checking when this action has finitely many orbits. We then use this method to give a complete classification for when $G$ is of type $F_4$. The $E_6, E_7,$ and $E_8$ cases will be treated in a subsequent paper.

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1 arXiv paper cite this in 2 sentences

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

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What it cites

Cites as background 1 paper
  • The references [ref] , [ref] , [ref] and [ref] deal with aspects of the geometry of these orbits and representation theory.

    Spherical multiple flags · Introduction · 0.99

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