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Higher su(N) tensor products

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J. Rasmussen, M.A. Walton

Mathematical Physics · Submitted 24 Feb 2001

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

The authors' main claim The solution is a set of inequalities in the Dynkin labels.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath-ph/0102031 (version 1)
Pith IDPWQ6CPOU, Pith's permanent record of this paper and its review
CitationJ. Rasmussen, M.A. Walton. "Higher su(N) tensor products." arXiv:math-ph/0102031 (2001). https://pith.science/paper/PWQ6CPOU
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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, 6,012 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.15 · compares with prior results 0.78 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We extend our recent results on ordinary su(N) tensor product multiplicities to higher su(N) tensor products. Particular emphasis is put on four-point couplings where the tensor product of four highest weight modules is considered. The number of times the singlet occurs in the decomposition is the associated multiplicity. In this framework, ordinary tensor products correspond to three-point couplings. As in that case, the four-point multiplicity may be expressed explicitly as a multiple sum measuring the discretised volume of a convex polytope. This description extends to higher-point couplings as well. We also address the problem of determining when a higher-point coupling exists, i.e., when the associated multiplicity is non-vanishing. The solution is a set of inequalities in the Dynkin labels.

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 We extend our recent results on ordinary su(N) tensor product multiplicities to higher su(N) tensor products. contribution 0.99 0.90 0.22 asserted 0.98
s1 Particular emphasis is put on four-point couplings where the tensor product of four highest weight modules is considered. contribution 0.99 0.66 0.07 asserted 0.89
s2 The number of times the singlet occurs in the decomposition is the associated multiplicity. background 0.66 0.22 0.08 asserted 1.00
s3 In this framework, ordinary tensor products correspond to three-point couplings. background 0.88 0.23 0.05 asserted 1.00
s4 As in that case, the four-point multiplicity may be expressed explicitly as a multiple sum measuring the discretised volume of a convex polytope. result 0.75 0.79 0.24 hedged possibility 0.95
s5 This description extends to higher-point couplings as well. contribution 0.46 0.67 0.09 asserted 0.99
s6 We also address the problem of determining when a higher-point coupling exists, i.e., when the associated multiplicity is non-vanishing. contribution 0.95 0.85 0.09 asserted 0.85
s7 The solution is a set of inequalities in the Dynkin labels. result 0.97 0.87 0.39 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

What was examined, and what was not

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not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • 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

We extend our recent results on ordinary su(N) tensor product multiplicities to higher su(N) tensor products. Particular emphasis is put on four-point couplings where the tensor product of four highest weight modules is considered. The number of times the singlet occurs in the decomposition is the associated multiplicity. In this framework, ordinary tensor products correspond to three-point couplings. As in that case, the four-point multiplicity may be expressed explicitly as a multiple sum measuring the discretised volume of a convex polytope. This description extends to higher-point couplings as well. We also address the problem of determining when a higher-point coupling exists, i.e., when the associated multiplicity is non-vanishing. The solution is a set of inequalities in the Dynkin labels.

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