Higher-Level Appell Functions, Modular Transformations, and Characters

@article{Semikhatov2005HigherLevelAF,
  title={Higher-Level Appell Functions, Modular Transformations, and Characters},
  author={A. M. Semikhatov and A. Taorimina and I. Yu. Tipunin},
  journal={Communications in Mathematical Physics},
  year={2005},
  volume={255},
  pages={469-512}
}
We study modular transformation properties of a class of indefinite theta series involved in characters of infinite-dimensional Lie superalgebras. The level-ℓ Appell functions satisfy open quasiperiodicity relations with additive theta-function terms emerging in translating by the “period.” Generalizing the well-known interpretation of theta functions as sections of line bundles, the function enters the construction of a section of a rank-(ℓ+1) bundle . We evaluate modular transformations of… 
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53 Citations
Highly Influential Citations
4
Background Citations
8
Methods Citations
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53 Citations

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