Schur đ-functions and the Capelli eigenvalue problem for the Lie superalgebra \gerđ(đ)
Bibliographic record
Abstract
Let \ger l\defi \ger q(n)\times \ger q(n) , where \ger q(n) denotes the queer Lie superalgebra. The associative superalgebra V V of type Q ( n ) Q(n) has a left and right action of \ger q(n) , and hence is equipped with a canonical \ger l -module structure. We consider a distinguished basis { D λ } \{D_\lambda \} of the algebra of \ger l -invariant super-polynomial differential operators on V V , which is indexed by strict partitions of length at most n n . We show that the spectrum of the operator D λ D_\lambda , when it acts on the algebra P ( V ) \mathscr P(V) of super-polynomials on V V , is given by the factorial Schur Q Q -functions of Okounkov and Ivanov. As an application, we show that the radial projections of the spherical super-polynomials (corresponding to the diagonal symmetric pair (\ger l,\ger m) , where \ger m\defi \ger q(n) ) of irreducible \ger l -submodules of P ( V ) \mathscr P(V) are the classical Schur Q Q -functions. As a further application, we compute the Harish-Chandra images of the Nazarov basis { C λ
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.016 | 0.003 |
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".