A Feigin-Frenkel theorem with n singularities

2023/01/16 by Luca Casarin, Casarin, Luca
Mathematics · #17B65 (Primary) 17B69 (Secondary) #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2301.06419

openalex publication_date 2023/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a simple Lie algebra g we consider an analogue of the affine algebra ^gk with n singularities, defined starting from the ring of functions on the n-pointed disk. We study the center of its completed enveloping algebra and prove an analogue of the Feigin-Frenkel theorem in this setting. In particular, we first give an algebraic description of the center by providing explicit topological generators; we then characterize the center geometrically as the ring of functions on the space of G^L-Opers over the n-pointed disk. Finally, we prove some factorization properties of our isomorphism, thus establishing a relation between our isomorphism and the usual isomorphism of Feigin-Frenkel.

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