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 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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".