Tensor category KLk(sl2n) via minimal affine W-algebras at the non-admissible level k=−[Formula presented]

Adamović D, Creutzig T, Perše O, Vukorepa I (2024)

Publication Type: Journal article

Publication year: 2024

Journal

Journal of Pure and Applied Algebra Elsevier

Book Volume: 228

Article Number: 107565

Journal Issue: 5

DOI: 10.1016/j.jpaa.2023.107565

Abstract

We prove that the Kazhdan-Lusztig category of slˆm at level k, KLk(slm), is a semi-simple, rigid braided tensor category for all even m≥4, and k=−[Formula presented]. Moreover, all modules in KLk(slm) are simple-currents and they appear in the decomposition of conformal embeddings glm↪slm+1 at level k=−[Formula presented]. For this we inductively identify minimal affine W-algebra Wk−1(slm+2,θ) as simple current extension of Lk(slm)⊗H⊗M, where H is the rank one Heisenberg vertex algebra, and M the singlet vertex algebra for c=−2. The proof uses previously obtained results for the tensor categories of singlet algebra. We also classify all irreducible ordinary modules for Wk−1(slm+2,θ). The semi-simple part of the category of Wk−1(slm+2,θ)–modules comes from KLk−1(slm+2), using quantum Hamiltonian reduction, but this W-algebra also contains indecomposable ordinary modules.

Involved external institutions

University of Zagreb / Sveučilište u Zagrebu HR Croatia (HR) University of Alberta CA Canada (CA)

How to cite

APA:

Adamović, D., Creutzig, T., Perše, O., & Vukorepa, I. (2024). Tensor category KLk(sl2n) via minimal affine W-algebras at the non-admissible level k=−[Formula presented]. Journal of Pure and Applied Algebra, 228(5). https://doi.org/10.1016/j.jpaa.2023.107565

MLA:

Adamović, Dražen, et al. "Tensor category KLk(sl2n) via minimal affine W-algebras at the non-admissible level k=−[Formula presented]." Journal of Pure and Applied Algebra 228.5 (2024).

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