HigherLevel Appell Functions, Modular Transformations, and Characters
Abstract
We study modular transformation properties of a class of indefinite theta series involved in characters of infinitedimensional Lie superalgebras. The levelℓ Appell functions satisfy open quasiperiodicity relations with additive thetafunction terms emerging in translating by the “period.” Generalizing the wellknown 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:

Communications in Mathematical Physics
 Pub Date:
 April 2005
 DOI:
 10.1007/s0022000412807
 arXiv:
 arXiv:math/0311314
 Bibcode:
 2005CMaPh.255..469S
 Keywords:

 Mathematics  Quantum Algebra;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 amsart++, xy, times. 46pp. References added, minor changes