Center of Affine Sl2|1at the Critical Level
Adamović D, Nakatsuka S (2025)
Publication Type: Journal article
Publication year: 2025
Journal
Book Volume: 2025
Article Number: rnaf212
Journal Issue: 14
DOI: 10.1093/imrn/rnaf212
Abstract
In this article, we shall describe the center of the universal affine vertex superalgebra Vκc(g) associated with g = sl2|1, gl2|1 at the critical level κc and prove the conjecture of A. Molev and E. Ragoucy [24] in this case. The center z(Vκc (sl2|1)) turns out to be isomorphic to the large level limit l → ∞ of a vertex subalgebra, called the parafermion vertex algebra Kl(sl2), of the affine vertex algebra Vl(sl2). The key ingredient of the proof is to understand the principal W-superalgebra Wκc(sl2|1) at the critical level. It relates the center z(Vκc(sl2|1)) to V∞(sl2) via the Kazama-Suzuki duality while it has a surprising coincidence with Vκc (gl1 |1), whose center has been recently described. Moreover, the centers z (Vκc (sl2|1)) and z(Wκc(sl2|1)) are proven to coincide as a byproduct. A general conjecture is proposed, which describes the center z(Vκc(sln|m)) with n > m as a large level limit of "the dual side", that is, the parafermion-type subalgebras of W-algebras Wl(sln,O[n-m1m]) associated with hook-type partitions [n - m,1m], known also as vertex algebras at the corner.
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APA:
Adamović, D., & Nakatsuka, S. (2025). Center of Affine Sl2|1at the Critical Level. International Mathematics Research Notices, 2025(14). https://doi.org/10.1093/imrn/rnaf212
MLA:
Adamović, Dražen, and Shigenori Nakatsuka. "Center of Affine Sl2|1at the Critical Level." International Mathematics Research Notices 2025.14 (2025).
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