Past the Highest-Weight, and What You Can Find There

1997/12/09 by A M Semikhatov, Semikhatov, A M · 1 citation
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #hep-th #math.QA #q-alg

paper · pdf · doi:10.48550/arxiv.q-alg/9712024

LaTeX 2e, 16pp. Talk presented at the NATO Advanced Research Workshop on Theoretical Physics `New Developments in Quantum Field Theory', June 14--20, 1997, Zakopane, and IV International Conference `Conformal Field Theories and Integrable Models', Chernogolovka, June 23--27, 1997

Abstract

The properties of highest-weight representations of the N=2 superconformal algebra in two dimensions can be considerably simplified when re-expressed in terms of relaxed ^sl(2) representations. This applies to the appearance of submodules and hence, of singular vectors, and to the structure of the embedding diagrams and the BGG-type resolution. I also discuss the realization of these representations in the bosonic string, where the generalized DDK prescription amounts to the requirement that the representations have a charged singular vector, and the role of the fermionic screening operator.

Cited by

• Generalized Verma modules over sl(m+1) induced from simple highest weight modules

Related

• Recent Results on N=2 Superconformal Algebras
• Verma Modules, Extremal Vectors, and Singular Vectors on the Non-Critical N=2 String Worldsheet
• Characters of the Unitarizable Highest Weight Modules over the N=2 Superconformal Algebras
• Free-Field Resolutions of the Unitary N=2 Super-Virasoro Representations
• Extremal unitary representations of big N=4 superconformal algebra