Braid group actions, Baxter polynomials, and affine quantum groups
Bibliographic record
Abstract
It is a classical result in representation theory that the braid group B g \mathscr {B}_\mathfrak {g} of a simple Lie algebra g \mathfrak {g} acts on any integrable representation of g \mathfrak {g} via triple products of exponentials in its Chevalley generators. In this article, we show that a modification of this construction induces an action of B g \mathscr {B}_\mathfrak {g} on the commutative subalgebra Y ℏ 0 ( g ) ⊂ Y ℏ ( g ) Y_\hbar ^{0}(\mathfrak {g})\subset Y_\hbar ^{}(\mathfrak {g}) of the Yangian by Hopf algebra automorphisms, which gives rise to a representation of the Hecke algebra of type g \mathfrak {g} on a flat deformation of the Cartan subalgebra h [ t ] ⊂ g [ t ] \mathfrak {h}[t]\subset \mathfrak {g}[t] . By dualizing, we recover a representation of B g \mathscr {B}_\mathfrak {g} constructed in the works of Y. Tan [ Braid group actions and tensor products for Yangians , Preprint, arXiv: 1510.01533 , 2015] and V. Chari [Int. Math. Res. Not. 7 (2002), pp. 357–382], which was used to obtain sufficient conditions for the cyclicity of any tensor product of irreducible representations of Y ℏ
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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) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.013 | 0.003 |
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".