Two-parameter quantum affine algebra of type G2(1), Drinfeld realization and vertex representation
Bibliographic record
Abstract
In this paper, we define the two-parameter quantum affine algebra for type G2(1) and give the (r, s)-Drinfeld realization of Ur,s(G2(1)), as well as establish and prove its Drinfeld isomorphism. We construct and verify explicitly the level-one vertex representation of two-parameter quantum affine algebra Ur,s(G2(1)), which also supports an evidence in nontwisted type G2(1) for the uniform defining approach via the two-parameter τ-invariant generating functions proposed in Hu and Zhang [Generating functions with τ-invariance and vertex representations of two-parameter quantum affine algebras Ur,s(ĝ): Simply laced cases e-print arXiv:1401.4925]
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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".