Multiplicative McKay Correspondence via Special McKay Quiver Moduli — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: The multiplicative McKay correspondence for surfaces refines the classical additive correspondence by encoding the representation ring's multiplicative structure via the derived category of the minimal resolution, with the Special McKay quiver construction providing an explicit moduli realization. | MATH: Classical McKay: for G ⊂ SL(2,ℂ), the minimal resolution Y → ℂ²/G has exceptional fibers indexed by nontrivial irreducible representations ρ_i, with intersection matrix given by the McKay quiver's Cartan matrix (A-D-E type). Multiplicative version (Fu): the derived category D^b(Y) ≅ D^b(ℂ²/G) as a tensor category requires a twisted product on the representation ring R(G) — specifically, the convolution product on G-equivariant K-theory K_G(ℂ²) ≅ R(G) must be deformed by the gerbe/braiding coming from the McKay quiver's orientation. Special McKay (arXiv:0704.3627): for singularity 1/r(1,a), the quiver Q_spec has vertices = "special" representations (those with dim = 1 or appea
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026multiplicative,
title = {{Multiplicative McKay Correspondence via Special McKay Quiver Moduli — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23610340},
url = {https://zenodo.org/records/23610340},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Multiplicative McKay Correspondence via Special McKay Quiver Moduli — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/24
PB - Zenodo
DO - 10.5281/zenodo.23610340
UR - https://zenodo.org/records/23610340
AB - FINDING: The multiplicative McKay correspondence for surfaces refines the classical additive correspondence by encoding the representation ring's multiplicative structure via the derived category of the minimal resolution, with the Special McKay quiver construction providing an explicit moduli realization. | MATH: Classical McKay: for G ⊂ SL(2,ℂ), the minimal resolution Y → ℂ²/G has exceptional fibers indexed by nontrivial irreducible representations ρ_i, with intersection matrix given by the McKay quiver's Cartan matrix (A-D-E type). Multiplicative version (Fu): the derived category D^b(Y) ≅ D^b(ℂ²/G) as a tensor category requires a twisted product on the representation ring R(G) — specifically, the convolution product on G-equivariant K-theory K_G(ℂ²) ≅ R(G) must be deformed by the gerbe/braiding coming from the McKay quiver's orientation. Special McKay (arXiv:0704.3627): for singularity 1/r(1,a), the quiver Q_spec has vertices = "special" representations (those with dim = 1 or appea Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -