{"id":"openai-math/Global-quantum-geometric-Langlands-at-irrational-level","pdf":"https://github.com/openai/math/blob/main/preprints/Global-quantum-geometric-Langlands-at-irrational-level-October-4-2026/quantum-langlands.pdf","url":"https://github.com/openai/math/tree/main/preprints/Global-quantum-geometric-Langlands-at-irrational-level-October-4-2026","tags":["geometric-langlands","d-modules","conformal-field-theory","representation-theory"],"score":0,"title":"Global quantum geometric Langlands at irrational level","domain":"Algebraic and complex geometry","family":"069","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"We prove the unramified quantum geometric Langlands equivalence for every connected simple complex algebraic group G and every level $`c\\in\\mathbb C\\setminus\\mathbb Q`$, including non-real levels. For every smooth projective connected complex curve X , it identifies the full twisted D -module categories on $`\\mathop{\\mathrm{Bun}}\\nolimits _G(X)`$ and $`\\mathop{\\mathrm{Bun}}\\nolimits _{G^\\vee}(X)`$ at the dual shifted levels c and $`-1/(rc)`$, where r is the lacing number. The equivalence uses the given global forms and includes all connected components.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":1,"published":"2026-10-04","reactions":{},"discussion":[{"url":"https://arxiv.org/abs/2610.18089","date":"2026-10-13","kind":"web","site":"arXiv.org","text":"AI has become increasingly helpful in scientific discovery, yet human expert review remains essential for those problems without reliable automated evaluation, posing a fundamental challenge as candidate generation scales beyond available review capacity. This paper studies verification under…","added":"2026-10-24","title":"One-Sided Verification Under Limited Expert Review","author":"Fan Nie, Haotian Ye, Shurui Liu, Zihao Wang et al."}],"formalized":false,"family_title":"Global quantum geometric Langlands at irrational level"}