Global Weyl Modules for Equivariant Map Algebras
Bibliographic record
Abstract
Equivariant map algebras are Lie algebras of algebraic maps from a scheme (or algebraic variety) to a target finite-dimensional Lie algebra (in the case of the current paper, we assume the latter is a simple Lie algebra) that are equivariant with respect to the action of a finite group. In the first part of this paper, we define global Weyl modules for equivariant map algebras satisfying a mild assumption. We then identify a commutative algebra |$\textbf {A}^{\lambda} _\Gamma $| that acts naturally on the global Weyl modules, which leads to a Weyl functor from the category of |$\textbf {A}^{\lambda} _{\Gamma} $|-modules to the category of modules for the equivariant map algebra in question. These definitions extend the ones previously given for generalized current algebras (i.e., untwisted map algebras) and twisted loop algebras. In the second part of the paper, we restrict our attention to equivariant map algebras where the group involved is abelian, acts on the target Lie algebra by diagram automorphisms, and freely on (the set of rational points of) the scheme. Under these additional assumptions, we prove that |$\textbf {A}^{\lambda}_{\Gamma} $| is finitely generated and the global Weyl module is a finitely generated |$\textbf {A}^{\lambda}_{\Gamma} $|-module. We also define local Weyl modules via the Weyl functor and prove that these coincide with the local Weyl modules defined directly in [18]. Finally, we show that |$\textbf {A}^{\lambda}_{\Gamma} $| is the algebra of coinvariants of the analogous algebra in the untwisted case.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".