arXiv:2504.02266v3

Knizhnik-Zamolodchikov equations in Deligne categories

Pavel Etingof, Ivan Motorin, Alexander Varchenko, Isaac Zhu

math.RTmath-phmath.QA

Paper metadata

Original submission: April 3, 2025
Latest revision: June 30, 2026 · version 3
Claimed MSC
arXiv categories: math.RT, math-ph, math.QA
Paper license: CC BY 4.0 ↗
Journal reference: Commun. Math. Phys. 407, 116 (2026)
DOI: 10.1007/s00220-026-05612-6 ↗

Abstract

We consider the Knizhnik-Zamolodchikov equations in Deligne Categories in the context of $(\mathfrak{gl}_m,\mathfrak{gl}_{n})$ and $(\mathfrak{so}_m,\mathfrak{so}_{2n})$ dualities. We derive integral formulas for the solutions in the first case and compute monodromy in both cases.

AI-generated audit

Audit summary

Not a correctness certificate. A green “no issues found” result may include yellow suspected typos or minor formal issues that do not affect substantive soundness. It means this audit found no unresolved substantive error under the stated criteria; it does not replace expert scrutiny or formal verification.

01StatementsNot yet audited

02ProofsNot yet audited

03NoveltyNot yet audited

No report has been generated for this paper in the local prototype.