Quantum Geometric Langlands via Fundamental Local Equivalence — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Gaitsgory–Lurie's "fundamental local equivalence" replaces Satake equivalence in quantum geometric Langlands, proven for most cases by Dhillon et al. (arXiv:1907.03204), extending to affine flag varieties.
MATH: - Core object: categorical equivalence between factorization modules (or D-modules on loop groups) and representations of the quantum group / Kac-Moody algebra at critical level. - Key structure: **quantum parameter** ψ (level) — the equivalence holds for generic ψ, degenerating at roots of unity where quantum groups become finite-dimensional. - The classical Satake equivalence: Rep(checkG) ≅ Perv(GrG) — replaced by a **local equivalence** involving **factorization algebras** and **affine flag varieties** (not just Grassmannians). - No explicit numerical constants appear in the abstract; the mathematics is categorical (∞-categories, ind-coherent sheaves, chiral algebras).
CONNECTION: - **Root systems*
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026quantum,
title = {{Quantum Geometric Langlands via Fundamental Local Equivalence — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23526427},
url = {https://zenodo.org/records/23526427},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum Geometric Langlands via Fundamental Local Equivalence — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/21
PB - Zenodo
DO - 10.5281/zenodo.23526427
UR - https://zenodo.org/records/23526427
AB - FINDING: Gaitsgory–Lurie's "fundamental local equivalence" replaces Satake equivalence in quantum geometric Langlands, proven for most cases by Dhillon et al. (arXiv:1907.03204), extending to affine flag varieties. MATH: - Core object: categorical equivalence between factorization modules (or D-modules on loop groups) and representations of the quantum group / Kac-Moody algebra at critical level. - Key structure: **quantum parameter** ψ (level) — the equivalence holds for generic ψ, degenerating at roots of unity where quantum groups become finite-dimensional. - The classical Satake equivalence: Rep(checkG) ≅ Perv(Gr_G) — replaced by a **local equivalence** involving **factorization algebras** and **affine flag varieties** (not just Grassmannians). - No explicit numerical constants appear in the abstract; the mathematics is categorical (∞-categories, ind-coherent sheaves, chiral algebras). CONNECTION: - **Root systems* Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -