Projective oscillator representations of sl(n+1|m) and osp(m|n+1)

Abstract

Motivated from understanding higher-dimensional supersymmetric conformal field theory, we study various inhomogeneous oscillator representations of $sl(n+1|m)$ and $osp(m|n+1)$ on supersymmetric polynomial algebras and on spaces of supersymmetric exponential–polynomial functions, analogous to the projective oscillator representations of $sl(n+1)$ and $sp(2m+2)$. In particular, we find the explicit structures of certain Harish-Chandra modules and Whittaker-type modules of these Lie superalgebras.

Keywords:

• Irreducible module
• ortho-symplectic Lie superalgebra
• oscillator representation
• special linear Lie superalgebra
• supersymmetric exponential–polynomial function
• supersymmetric polynomial algebra

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 17B10
• Secondary 17B20

Additional information

Funding

Ling Chen was supported by NSFC Grant 11401559 and UCAS Grant Y55202HY00. Xiaoping Xu was supported by NSFC Grants 11671381 and 11321101.