Bibliographic record
Abstract
Let 𝔤 be a classical Lie superalgebra of type I or a Cartan-type Lie superalgebra W ( n ). We study weight 𝔤-modules using a method inspired by Mathieu's classification of the simple weight modules with finite weight multiplicities over reductive Lie algebras, [Mathieu O.: Classification of irreducible weight modules. Ann. Inst. Fourier 50 (2000), 537–592]. Our approach is based on the fact that every simple weight 𝔤-module with finite weight multiplicities is obtained via a composition of a twist and localization from a highest weight module. This allows us to transfer many results for category 𝒪 modules to the category of weight modules with finite weight multiplicities. As a main application of the method we reduce the problems of finding a 𝔤 0 -composition series and a character formula for all simple weight modules to the same problems for simple highest weight modules. In this way, using results of Serganova we obtain a character formula for all simple weight W ( n )-modules and all simple atypical nonsingular -modules. Some of our results are new already in the case of a classical reductive Lie algebra 𝔤.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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.
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".