Factorization Algebras Unify Quantum Geometric Langlands — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Quantum geometric Langlands is being reformulated via factorization algebras and local equivalences, bridging affine flag varieties, quantum groups at roots of unity, and cotangent bundles of partial flag varieties — a convergence of representation theory, algebraic geometry, and number theory.
MATH: - **Roots of unity**: q = e2π i / ℓ (or ℓ-th root), central to quantum group Uq(g) specialization. - **Kazhdan–Lusztig equivalence**: Rep(Uq(g)) ≅ Category of modules over affine Lie algebra at negative level — extended by Gaitsgory via factorization algebras. - **Affine flag variety**: ℱℓ = G(ℂ((t)))/I, where I is Iwahori subgroup; its factorization modules encode ℓ-adic sheaves / D-modules. - **Cotangent bundle compactification**: T*G/P embedded in affine Schubert variety — relates to conormal varieties of Schubert divisors (arXiv:1712.001
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026factorization,
title = {{Factorization Algebras Unify Quantum Geometric Langlands — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23635391},
url = {https://zenodo.org/records/23635391},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Factorization Algebras Unify Quantum Geometric Langlands — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/25
PB - Zenodo
DO - 10.5281/zenodo.23635391
UR - https://zenodo.org/records/23635391
AB - FINDING: Quantum geometric Langlands is being reformulated via factorization algebras and local equivalences, bridging affine flag varieties, quantum groups at roots of unity, and cotangent bundles of partial flag varieties — a convergence of representation theory, algebraic geometry, and number theory. MATH: - **Roots of unity**: q = e^2π i / ℓ (or ℓ-th root), central to quantum group U_q(g) specialization. - **Kazhdan–Lusztig equivalence**: Rep(U_q(g)) ≅ Category of modules over affine Lie algebra at negative level — extended by Gaitsgory via factorization algebras. - **Affine flag variety**: ℱℓ = G(ℂ((t)))/I, where I is Iwahori subgroup; its factorization modules encode ℓ-adic sheaves / D-modules. - **Cotangent bundle compactification**: T^*G/P embedded in affine Schubert variety — relates to conormal varieties of Schubert divisors (arXiv:1712.001 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -