PreprintCC BY-NC-SA 4.0arXiv
Gaudin from Cherednik
Abstract
Let W be a complex reflection group and X the De Concini-Procesi wonderful model of its reflection arrangement. Inside Etingof's sheaf of Cherednik algebras on X we define a subsheaf generated by the Dunkl operators that extend the standard ones on the hyperplane complement. We conjecture that at t=0 the image of the logarithmic vector fields in a natural module over this subsheaf is the sheaf of Gaudin algebras on X defined by Aguirre, extending a construction of Bonnafé and Rouquier from the hyperplane complement to X. We prove the conjecture for W=S3.
Related
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BibTeX
@misc{mcmillan2026gaudin,
title = {{Gaudin from Cherednik}},
author = {Matthew McMillan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20146},
eprint = {2610.20146},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20146},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Gaudin from Cherednik
AU - Matthew McMillan
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20146
UR - https://arxiv.org/abs/2610.20146
AB - Let W be a complex reflection group and X the De Concini-Procesi wonderful model of its reflection arrangement. Inside Etingof's sheaf of Cherednik algebras on X we define a subsheaf generated by the Dunkl operators that extend the standard ones on the hyperplane complement. We conjecture that at t=0 the image of the logarithmic vector fields in a natural module over this subsheaf is the sheaf of Gaudin algebras on X defined by Aguirre, extending a construction of Bonnafé and Rouquier from the hyperplane complement to X. We prove the conjecture for W=S_3.
ER -