Braid groups and Baxter polynomials
Bibliographic record
Abstract
It is well known that the braid group of a simple Lie algebra acts on its integrable representations via products of exponentials of its Chevalley generators. In particular, the Yangian is an integrable representation, so there is an action of the braid group on this space. We show that modifying this action induces an action of the braid group on a certain commutative subalgebra of the Yangian by Hopf algebra automorphisms. By dualizing this modified action, we recover an action of the braid group on tuples of rational functions defined in the work of Y. Tan. Using this dual action, we prove a conjecture of S. Gautam and C. Wendlandt that the two sufficient conditions for the tensor product of finite-dimensional irreducible representations of the Yangian to be cyclic are identical. One of these conditions involves the aforementioned action of the braid group on rational functions, and the other involves roots of the Baxter polynomials, which have many interesting properties and ties to mathematical physics.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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 teacher head, 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".