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Record W3101317332 · doi:10.1090/conm/711/14301

Cosets of the 𝒲^{𝓀}(𝔰𝔩₄,𝔣_{𝔰𝔲𝔟𝔯𝔢𝔤})-algebra

2018· other· en· W3101317332 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueContemporary mathematics - American Mathematical Society · 2018
Typeother
Languageen
FieldMathematics
TopicAdvanced Operator Algebra Research
Canadian institutionsUniversity of Alberta
Fundersnot available
KeywordsCombinatoricsQuotientSubalgebraVertex operator algebraTensor productCosetMathematicsPhysicsLattice (music)NilpotentAlgebra over a fieldCurrent algebraPure mathematicsJordan algebra

Abstract

fetched live from OpenAlex

Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper W Superscript k Baseline left-parenthesis German s German l Subscript 4 Baseline comma f Subscript subreg Baseline right-parenthesis"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">W</mml:mi> </mml:mrow> <mml:mi>k</mml:mi> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="fraktur">s</mml:mi> <mml:mi mathvariant="fraktur">l</mml:mi> </mml:mrow> <mml:mn>4</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>f</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext>subreg</mml:mtext> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathcal {W}^k(\mathfrak {sl}_4, f_{\text {subreg}})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be the universal <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper W"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">W</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathcal {W}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -algebra associated to <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="German s German l Subscript 4"> <mml:semantics> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="fraktur">s</mml:mi> <mml:mi mathvariant="fraktur">l</mml:mi> </mml:mrow> <mml:mn>4</mml:mn> </mml:msub> <mml:annotation encoding="application/x-tex">\mathfrak {sl}_4</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with its subregular nilpotent element, and let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper W Subscript k Baseline left-parenthesis German s German l Subscript 4 Baseline comma f Subscript subreg Baseline right-parenthesis"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">W</mml:mi> </mml:mrow> <mml:mi>k</mml:mi> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="fraktur">s</mml:mi> <mml:mi mathvariant="fraktur">l</mml:mi> </mml:mrow> <mml:mn>4</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>f</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext>subreg</mml:mtext> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathcal {W}_k(\mathfrak {sl}_4, f_{\text {subreg}})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be its simple quotient. There is a Heisenberg subalgebra <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper H"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">H</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathcal {H}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> , and we denote by <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper C Superscript k"> <mml:semantics> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">C</mml:mi> </mml:mrow> <mml:mi>k</mml:mi> </mml:msup> <mml:annotation encoding="application/x-tex">\mathcal {C}^k</mml:annotation> </mml:semantics> </mml:math> </inline-formula> the coset <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="Com left-parenthesis script upper H comma script upper W Superscript k Baseline left-parenthesis German s German l Subscript 4 Baseline comma f Subscript subreg Baseline right-parenthesis right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mtext>Com</mml:mtext> <mml:mo stretchy="false">(</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">H</mml:mi> </mml:mrow> <mml:mo>,</mml:mo> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">W</mml:mi> </mml:mrow> <mml:mi>k</mml:mi> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="fraktur">s</mml:mi> <mml:mi mathvariant="fraktur">l</mml:mi> </mml:mrow> <mml:mn>4</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>f</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext>subreg</mml:mtext> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\text {Com}(\mathcal {H}, \mathcal {W}^k(\mathfrak {sl}_4, f_{\text {subreg}}))</mml:annotation> </mml:semantics> </mml:math> </inline-formula> , and by <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper C Subscript k"> <mml:semantics> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">C</mml:mi> </mml:mrow> <mml:mi>k</mml:mi> </mml:msub> <mml:annotation encoding="application/x-tex">\mathcal {C}_k</mml:annotation> </mml:semantics> </mml:math> </inline-formu

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.002
metaresearch head score (Gemma)0.003
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Science and technology studies, Insufficient payload (model declined to judge)
Consensus categoriesMeta-epidemiology (narrow), Insufficient payload (model declined to judge)
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Not applicable · Consensus signal: none
GenreCandidate signal: Other · Consensus signal: Other
Teacher disagreement score0.705
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.003
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0030.002
Bibliometrics0.0000.002
Science and technology studies0.0000.005
Scholarly communication0.0000.000
Open science0.0030.001
Research integrity0.0010.001
Insufficient payload (model declined to judge)0.0060.001

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.057
GPT teacher head0.349
Teacher spread0.292 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it