Relatively Supercuspidal Representations of the Symplectic p-adic Groups
Bibliographic record
Abstract
In this thesis, we construct in a concrete manner a family of non-supercuspidal, relatively supercuspidal representations of symplectic p-adic groups, based on the work of Murnaghan. We cover the symmetric pairs (Sp(4n,F), Sp(2n,E)), (Sp(2n,E), Sp(2n,F)) and (Sp(2n,F), Sp(2k,F) x Sp(2(n-k),F)) where F is a p-adic field of odd residual characteristic, and E is a quadratic field extension of F. We also look at the symmetric pairs (Sp(2n,F), GL(n,F)) and (Sp(2n,F), U(n,E/F,ε)) for ε an invertible Hermitian matrix over E/F. For these additional pairs, the above construction doesn't result in any non-supercuspidal, relatively supercuspidal representations (despite these pairs admitting distinguished supercuspidals). We end with an in-depth look at the case of Sp(2,F) = SL(2,F). We show that in this low-rank example, for all of the above pairs, all irreducible relatively supercuspidal representations of SL2(F) are either supercuspidal or obtained from our construction. In particular, all irreducible H-relatively supercuspidal representations of SL(2,F), for H either GL(1,F) or U(1,E/F,ε), are supercuspidal.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.003 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| 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".