An equivalence between truncations of categorified quantum groups and Heisenberg categories
Bibliographic record
Abstract
We introduce a simple diagrammatic 2-category 𝒜 that categorifies the image of the Fock space representation of the Heisenberg algebra and the basic representation of 𝔰𝔩 ∞ . We show that 𝒜 is equivalent to a truncation of the Khovanov–Lauda categorified quantum group 𝒰 of type A ∞ , and also to a truncation of Khovanov’s Heisenberg 2-category ℋ . This equivalence is a categorification of the principal realization of the basic representation of 𝔰𝔩 ∞ . As a result of the categorical equivalences described above, certain actions of ℋ induce actions of 𝒰 , and vice versa. In particular, we obtain an explicit action of 𝒰 on representations of symmetric groups. We also explicitly compute the Grothendieck group of the truncation of ℋ . The 2-category 𝒜 can be viewed as a graphical calculus describing the functors of i -induction and i -restriction for symmetric groups, together with the natural transformations between their compositions. The resulting computational tool is used to give simple diagrammatic proofs of (apparently new) representation theoretic identities.
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.
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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 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".