<i>D</i>-functions and immanants of unitary matrices and submatrices
Bibliographic record
Abstract
Motivated by recent results in multiphoton interferometry, we expand a result of Kostant on immanants of an arbitrary m × m unitary matrix T ∈ SU ( m ) to the submatrices of T . Specifically, we show that immanants of principal submatrices of a unitary matrix T are a sum ∑ t D t t ( λ ) ( Ω ) of the diagonal D -functions of group element Ω, with t determined by the choice of submatrix, and the irrep ( λ ) determined by the immanant under consideration. We also provide evidence that this result extends to some submatrices that are not principal diagonal, and we discuss how this result can be extended to cases where T carries an SU( m ) representation that is different from the defining representation.
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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 | 0.000 |
| 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 | 0.001 |
| 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 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".