Integrable Highest Weight Modules over Affine Superalgebras and Appell's Function
By V. Kac, M. Wakimoto. 2000
197 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/89905e3ee440852737cd86301d1a0d4adfbf48c0
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In Algebra and Number Theory
In Discrete Mathematics and Combinatorics
In Geometry and Topology
Citations in the corpus
- Kac–Moody Superalgebras and Integrability (2011, methodology): “Representation theory of affine superalgebras has interesting applications in physics and number theory (see [11] and [12]).”
- Unearthing the visions of a master: harmonic Maass forms and number theory (2008, unknown): “…the author, Andrews, Eguchi, Hikami, Kac, Lawrence, Malmendier, Mellit, Okada, Wakimoto, and Zagier [15] [18] [21] [26] [92] [120] [121] [122] [130] [131] [144] [152] [153] [211] apply this theory to: • Donaldson invariants • Gauge theory • Representation theory of Lie superalgebras • Knot theory…”
- Logarithmic conformal field theory: beyond an introduction (2013, background): “We note that mock modular forms in general seem to be closely tied to atypical characters of affine Lie superalgebras, see [141–143].”