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

Authors
Kac, VG Wakimoto, M
Citation
Vg. Kac et M. Wakimoto, Integrable highest weight modules over affine superalgebras and Appell's function, COMM MATH P, 215(3), 2001, pp. 631-682
Citations number
23
Categorie Soggetti
Physics
Journal title
COMMUNICATIONS IN MATHEMATICAL PHYSICS
ISSN journal
00103616 → ACNP
Volume
215
Issue
3
Year of publication
2001
Pages
631 - 682
Database
ISI
SICI code
0010-3616(200101)215:3<631:IHWMOA>2.0.ZU;2-P
Abstract
We classify integrable irreducible highest weight representations of non-tw isted affine Lie superalgebras. We give a free field construction in the le vel 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 character s are expressed in terms of the Appell elliptic function. Our results demon strate that the representation theory of affine Lie superalgebras is quite different from that of affine Lie algebras.