Meromorphic tensor equivalence for Yangians and quantum loop algebras
Bibliographic record
Abstract
Let g be a complex semisimple Lie algebra, and Y ħ ( g ) , U q ( L g ) the corresponding Yangian and quantum loop algebra, with deformation parameters related by q = e π ι ħ . When ħ is not a rational number, we constructed in Gautam and Toledano Laredo (J. Am. Math. Soc. 29:775, 2016) a faithful functor Γ from the category of finite-dimensional representations of Y ħ ( g ) to those of U q ( L g ) . The functor Γ is governed by the additive difference equations defined by the commuting fields of the Yangian, and restricts to an equivalence on a subcategory of Rep fd ( Y ħ ( g ) ) defined by choosing a branch of the logarithm. In this paper, we construct a tensor structure on Γ and show that, if | q | ≠ 1 , it yields an equivalence of meromorphic braided tensor categories, when Y ħ ( g ) and U q ( L g ) are endowed with the deformed Drinfeld coproducts and the commutative part of their universal R -matrices. This proves in particular the Kohno–Drinfeld theorem for the abelian q KZ equations defined by Y ħ ( g ) . The tensor structure arises from the abelian q KZ equations defined by an appropriate regularisation of the commutative part of the R -matrix of Y ħ ( 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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.010 | 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".