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An algebraic geometric model of an action of the face monoid associated to a Kac-Moody group on its building

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Claus Mokler

Representation Theory · Submitted 27 Jun 2009

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

The authors' main claim Now we give an algebraic geometric model of one of these actions of the face monoid.

how it is stated · asserted 1.00 read the record →

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arXiv ID0906.5059 (version 3)
Pith IDKVLRNJLO, Pith's permanent record of this paper and its review
CitationClaus Mokler. "An algebraic geometric model of an action of the face monoid associated to a Kac-Moody group on its building." arXiv:0906.5059 (2009). https://pith.science/paper/KVLRNJLO
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,866 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.64 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

The face monoid described in [M1] acts on the integrable highest weight modules of a symmetrizable Kac-Moody algebra. It has similar structural properties as a reductive algebraic monoid whose unit group is a Kac-Moody group. We found in [M5] two natural extensions of the action of the Kac-Moody group on its building to actions of the face monoid on the building. Now we give an algebraic geometric model of one of these actions of the face monoid. The building is obtained as a part of the spectrum of homogeneous prime ideals of the Cartan algebra of the Kac-Moody group. We describe the full spectrum of homogeneous prime ideals of the Cartan algebra.

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 face monoid described in [M1] acts on the integrable highest weight modules of a symmetrizable Kac-Moody algebra. background 1.00 0.09 0.06 asserted 1.00
s1 It has similar structural properties as a reductive algebraic monoid whose unit group is a Kac-Moody group. background 0.94 0.12 0.06 asserted 0.99
s2 We found in [M5] two natural extensions of the action of the Kac-Moody group on its building to actions of the face monoid on the building. background 0.73 0.80 0.10 asserted 1.00
s3 Now we give an algebraic geometric model of one of these actions of the face monoid. contribution 0.99 0.94 0.39 asserted 1.00
s4 The building is obtained as a part of the spectrum of homogeneous prime ideals of the Cartan algebra of the Kac-Moody group. method 0.67 0.43 0.14 asserted 1.00
s5 We describe the full spectrum of homogeneous prime ideals of the Cartan algebra. contribution 0.86 0.93 0.19 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98.

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  • C citations
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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

The face monoid described in [M1] acts on the integrable highest weight modules of a symmetrizable Kac-Moody algebra. It has similar structural properties as a reductive algebraic monoid whose unit group is a Kac-Moody group. We found in [M5] two natural extensions of the action of the Kac-Moody group on its building to actions of the face monoid on the building. Now we give an algebraic geometric model of one of these actions of the face monoid. The building is obtained as a part of the spectrum of homogeneous prime ideals of the Cartan algebra of the Kac-Moody group. We describe the full spectrum of homogeneous prime ideals of the Cartan algebra.

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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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