Cosets of Bershadsky–Polyakov algebras and rational W -algebras of type A

Arakawa T, Creutzig T, Linshaw AR (2017)

Publication Type: Journal article

Publication year: 2017

Journal

Selecta Mathematica-New Series Springer Verlag (Germany)

Book Volume: 23

Pages Range: 2369-2395

Journal Issue: 4

DOI: 10.1007/s00029-017-0340-8

Abstract

The Bershadsky–Polyakov algebra is the W-algebra associated to sl3 with its minimal nilpotent element fθ. For notational convenience we define Wℓ= Wℓ-3/2(sl3, fθ). The simple quotient of Wℓ is denoted by Wℓ, and for ℓ a positive integer, Wℓ is known to be C2-cofinite and rational. We prove that for all positive integers ℓ, Wℓ contains a rank one lattice vertex algebra VL, and that the coset Cℓ= Com (VL, Wℓ) is isomorphic to the principal, rational W(sl2ℓ) -algebra at level (2 ℓ+ 3) / (2 ℓ+ 1) - 2 ℓ. This was conjectured in the physics literature over 20 years ago. As a byproduct, we construct a new family of rational, C2-cofinite vertex superalgebras from Wℓ.

Involved external institutions

Kyoto University / 京都大学 Kyōto daigaku JP Japan (JP) University of Alberta CA Canada (CA) University of Denver US United States (USA) (US)

How to cite

APA:

Arakawa, T., Creutzig, T., & Linshaw, A.R. (2017). Cosets of Bershadsky–Polyakov algebras and rational W -algebras of type A. Selecta Mathematica-New Series, 23(4), 2369-2395. https://doi.org/10.1007/s00029-017-0340-8

MLA:

Arakawa, Tomoyuki, Thomas Creutzig, and Andrew R. Linshaw. "Cosets of Bershadsky–Polyakov algebras and rational W -algebras of type A." Selecta Mathematica-New Series 23.4 (2017): 2369-2395.

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