Representation theory of 𝐿_{𝑘}(𝔬𝔰𝔭(1|2)) from vertex tensor categories and Jacobi forms
Bibliographic record
Abstract
The purpose of this work is to illustrate in a family of interesting examples how to study the representation theory of vertex operator superalgebras by combining the theory of vertex algebra extensions and modular forms. Let L k ( o s p ( 1 | 2 ) ) L_k\left (\mathfrak {osp}(1 | 2)\right ) be the simple affine vertex operator superalgebra of o s p ( 1 | 2 ) \mathfrak {osp}(1|2) at an admissible level k k . We use a Jacobi form decomposition to see that this is a vertex operator superalgebra extension of L k ( s l 2 ) ⊗ Vir ( p , ( p + p ′ ) / 2 ) L_k(\mathfrak {sl}_2)\otimes \text {Vir}(p, (p+p’)/2) where k + 3 / 2 = p / ( 2 p ′ ) k+3/2=p/(2p’) and Vir ( u , v ) \text {Vir}(u, v) denotes the regular Virasoro vertex operator algebra of central charge c = 1 − 6 ( u − v
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.011 | 0.002 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".