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

• Tomoyuki Arakawa ^[1] ; Andrew R. Linshaw ^[2]
  1. [1] Kyoto University

     Kyoto University

     Kamigyō-ku, Japón

     
  2. [2] University of Denver

     University of Denver

     Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 4, 2017, págs. 2369-2395
• Idioma: inglés
• DOI: 10.1007/s00029-017-0340-8
• Enlaces
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• Resumen

  • The Bershadsky–Polyakov algebra is the W-algebra associated to sl3 with its minimal nilpotent element fθ . For notational convenience we define W = W−3/2(sl3, fθ ). The simple quotient ofW is denoted byW, and for a positive integer,W is known to beC2-cofinite and rational.We prove that for all positive integers , W contains a rank one lattice vertex algebra VL , and that the coset C = Com(VL , W) is isomorphic to the principal, rational W(sl2)-algebra at level(2+3)/(2+1)−2. 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 W. Keywords Vert