Integrable highest weight modules over affine superalgebras and Appell's function

Details Integrable highest weight modules over affine superalgebras and Appell's function Integrable highest weight modules over affine superalgebras and Appell's function

2000-06-07

arxiv.org/abs/math-ph/0006007v1

Physics

Mathematical Physics

54 pages

Scientific paper

10.1007/s002200000315

We classify integrable irreducible highest weight representations of non-twisted affine Lie superalgebras. We give a free field construction in the level~1 case. The analysis of this construction shows, in particular, that in the simplest case of the $s\ell (2|1)$ level~1 affine superalgebra the characters are expressed in terms of the Appell elliptic function. Our results demonstrate that the representation theory of affine Lie superalgebras is quite different from that of affine Lie algebras.

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