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Record W4313906315 · doi:10.4171/dm/679

Weighted Khovanov-Lauda-Rouquier Algebras

2019· article· en· W4313906315 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

VenueDocumenta Mathematica · 2019
Typearticle
Languageen
FieldMathematics
TopicAlgebraic structures and combinatorial models
Canadian institutionsPerimeter InstituteUniversity of Waterloo
FundersNational Science Foundation
KeywordsMathematicsPure mathematicsAlgebra over a fieldCombinatorics

Abstract

fetched live from OpenAlex

In this paper, we define a generalization of Khovanov–Lauda–Rouquier algebras which we call weighted Khovanov–Lauda–Rouquier algebras . We show that these algebras carry many of the same structures as the original Khovanov–Lauda–Rouquier algebras, including induction and restriction functors which induce a twisted bialgebra structure on their Grothendieck groups. We also define natural steadied quotients of these algebras, which in an important special cases give categorical actions of an associated Lie algebra. These include the algebras categorifying tensor products and Fock spaces defined by the author and C. Stroppel [ B. Webster , Mem. Am. Math. Soc. 1191, iii-vi, 146 p. (2017; Zbl 07000045), p. 141, and C. Stroppel and B. Webster , “Quiver Schur algebras and q -Fock space”, Preprint, ]. For symmetric Cartan matrices, weighted KLR algebras also have a natural geometric interpretation as convolution algebras, generalizing that for the original KLR algebras by M. Varagnolo and E. Vasserot [J. Reine Angew. Math. 659, 67–100 (2011; Zbl 1229.17019)]; this result has positivity consequences important in the theory of crystal bases. In this case, we can also relate the Grothendieck group and its bialgebra structure to the Hall algebra of the associated quiver.

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)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Insufficient payload (model declined to judge)
Consensus categoriesInsufficient payload (model declined to judge)
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.045
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0110.002

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 head0.018
GPT teacher head0.291
Teacher spread0.273 · 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