Branching laws for Stein's complementary series and Speh representations of GL(2n,R)
Bibliographic record
Abstract
We obtain the explicit direct integral decomposition of Stein's complementary series representations and Speh representations of GL(2n,R) when restricted to the subgroup GL(2n-1,R). The decomposition is a direct integral of unitarily induced representations from a maximal parabolic subgroup of GL(2n-1,R) with Levi factor GL(2n-2,R)xGL(1,R), where the induction data consists of a complementary series or Speh representation of the factor GL(2n-2,R) with the same parameter as the one of GL(2n,R) and a character of GL(1,R). These results are in line with the theory of adduced representations. The main tools in the proof are two families of symmetry breaking operators between degenerate series representations of GL(2n,R) and GL(2n-1,R) whose meromorphic properties are studied in great detail.
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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 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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".