Abstract:We prove a factorizable version of the Feigin-Frenkel theorem on the center of the completed enveloping algebra of the affine Kac-Moody algebra attached to a simple Lie algebra at the critical level. On any smooth curve C we consider a sheaf of complete topological Lie algebras whose fiber at any point is the usual affine algebra at the critical level and consider its sheaf of completed enveloping algebras. We show that the center of this sheaf is a factorization algebra and establish that it is canonically isomorphic, in a factorizable manner, with the factorization algebra of functions on Opers on the pointed disk for the Langlands dual Lie algebra.
| Subjects: | Representation Theory (math.RT) |
| MSC classes: | 17B65, 17B69 |
| Cite as: | arXiv:2501.09589 [math.RT] |
| (or arXiv:2501.09589v4 [math.RT] for this version) | |
| https://doi.org/10.48550/arXiv.2501.09589 arXiv-issued DOI via DataCite |
From: Luca Casarin [view email]
[v1]
Thu, 16 Jan 2025 15:14:42 UTC (76 KB)
[v2]
Sun, 22 Jun 2025 09:36:04 UTC (115 KB)
[v3]
Fri, 26 Sep 2025 19:45:30 UTC (116 KB)
[v4]
Fri, 22 May 2026 13:09:11 UTC (108 KB)
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