The local character expansion as branchingrules : nilpotent cones and the case of SL(2)
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Bibliographic record
Abstract
We show there exist representations of each maximal compact subgroup K of the padic group G = SL(2, F ), attached to each nilpotent coadjoint orbit, such that every irreducible representation of G, upon restriction to a suitable subgroup of K, is a sum of these five representations in the Grothendieck group.This is a representation-theoretic analogue of the analytic local character expansion due to Harish-Chandra and Howe.Moreover, we show for general connected reductive groups that the wave front set of many irreducible positive-depth representations of G are completely determined by the nilpotent support of their unrefined minimal K-types.where G x,r+ is the Moy-Prasad filtration subgroup of G x of depth r+, and the sum is over all nilpotent orbits in g * .
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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 | 0.002 | 0.001 |
| 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 it