Basic polynomial invariants, fundamental representations and the Chern class map
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Bibliographic record
Abstract
Consider a crystallographic root system together with its Weyl group W acting on the weight lattice \Lambda . Let \mathbb Z[\Lambda]^W and S(\Lambda)^W be the W -invariant subrings of the integral group ring \mathbb Z[\Lambda] and the symmetric algebra S(\Lambda) respectively. A celebrated result by Chevalley says that \mathbb Z[\Lambda]^W is a polynomial ring in classes of fundamental representations \rho_1,...,\rho_n and S(\Lambda)^W\otimes{Q} is a polynomial ring in basic polynomial invariants q_1,...,q_n . In the present paper we establish and investigate the relationship between \rho_i 's and q_i 's over the integers. As an application we provide estimates for the torsion of the Grothendieck \gamma -filtration and the Chow groups of some twisted flag varieties up to codimension 4.
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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 | 0.001 | 0.000 |
| 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 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 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 it