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Record W2042346138 · doi:10.1007/s10240-004-0020-z

Functoriality for the classical groups

2004· article· fr· W2042346138 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenuePublications mathématiques de l IHÉS · 2004
Typearticle
Languagefr
FieldMathematics
TopicAdvanced Algebra and Geometry
Canadian institutionsUniversity of Toronto
Fundersnot available
KeywordsMathematics

Abstract

fetched live from OpenAlex

Functoriality is one of the most central questions in the theory of automor-phic forms and representations [1,2,35,36]. Locally and globally, it is a manifesta-tion of Langlands ’ formulation of a non-abelian class field theory. Now known as the Langlands correspondence, this formulation of class field theory can be viewed as giving an arithmetic parameterization of local or automorphic representations in terms of admissible homomorphisms of (an appropriate analogue) of the Weil-Deligne group into the Langlands dual group or L-group. When this conjectural parameterization is combined with natural homomorphisms of the L-groups it pre-dicts a transfer or lifting of local or automorphic representations of two reductive algebraic groups. As a purely automorphic expression of a global non-abelian class field theory, global functoriality is inherently an arithmetic process. In this paper we establish global functoriality from the split classical groups Gn = SO2n+1, SO2n, or Sp2n to an appropriate general linear group GLN, associated to the natural embedding of L-groups, for globally generic cuspidal representations π of Gn(A) over a number field k. We had previously presented functoriality for

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.004
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Methods · Consensus signal: Methods
Teacher disagreement score0.376
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.004
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.001
Science and technology studies0.0010.000
Scholarly communication0.0000.001
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.050
GPT teacher head0.339
Teacher spread0.289 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it