On the spectrum of geometric operators on Kähler manifolds
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Bibliographic record
Abstract
On a compact Kähler manifold, there is a canonical actionof a Lie-superalgebra on the space of differential forms. It is generatedby the differentials, the Lefschetz operator, and the adjoints of these operators.We determine the asymptotic distribution of irreducible representationsof this Lie-superalgebra on the eigenspaces of the Laplace--Beltrami operator.Because of the high degree of symmetry, the Laplace--Beltrami operator on formscan not be quantum ergodic. We show that, after taking these symmetries intoaccount, quantum ergodicity holds for the Laplace--Beltrami operator andfor the Spin$^\cbb$-Dirac operators if the unitary frame flow is ergodic. Theassumptions for our theorem are known to be satisfiedfor instance for negatively curved Kähler manifolds of odd complex dimension.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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