Higher-Level Appell Functions, Modular Transformations, and Characters
Abstract
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 the functions and construct the action of an SL(2,&Z;) subgroup that leaves the section of constructed from invariant.
- Publication:
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Communications in Mathematical Physics
- Pub Date:
- April 2005
- DOI:
- 10.1007/s00220-004-1280-7
- arXiv:
- arXiv:math/0311314
- Bibcode:
- 2005CMaPh.255..469S
- Keywords:
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- Mathematics - Quantum Algebra;
- High Energy Physics - Theory;
- Mathematical Physics
- E-Print:
- amsart++, xy, times. 46pp. References added, minor changes