On resolution of highest weight modules over the N=2 superconformal algebra

2018/10/31 by Koshida, Shinji, Sato, Ryo
#17B68 #81R10 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary 17B69 #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Secondary 17B10

paper · doi:10.48550/arxiv.1810.13147

Abstract

In this paper we construct Bernstein--Gelfand--Gelfand type resolution of simple highest weight modules over the simple N=2 vertex operator superalgebra of central charge c_p,p'=3(1-(2p')/(p)) by means of the Kazama--Suzuki coset construction. As an application, we compute the twisted Zhu algebras of the simple N=2 vertex operator superalgebra. We also compute the Frenkel--Zhu bimodule structure associated with a certain simple highest weight module of central charge c_3,2=-1.

Related

• Representations of N=2 superconformal vertex algebra
• Characters of the Unitarizable Highest Weight Modules over the N=2 Superconformal Algebras
• Equivalences between weight modules via N=2 coset constructions
• On non-weight representations of the N=2 superconformal algebras
• Fusion rules and rigidity for weight modules over the simple admissible affine \mathfraksl(2) and N=2 superconformal vertex operator superalgebras