Integrable Highest Weight Modules over Affine Superalgebras and Appell's Function |
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| Authors: | Victor G. Kac Minoru Wakimoto |
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| Affiliation: | Department of Mathematics, M.I.T., Cambridge, MA 02139, USA.?E-mail: kac@math.mit.edu, US
Graduate School of Mathematics, Kyushu University, Fukuoka 812-81, Japan.?E-mail: wakimoto@math.kyushu-u.ac.jp, JP
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| Abstract: | 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 sℓ (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. Received: 17 April 2000 / Accepted: 7 July 2000 |
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