A kind of character for loop group representations (e.g. Gordon 08, def 5.11).
The Weyl-Kac character formula expresses it for integrable highest weigth representations in terms of the weights (e.g. Gordon 08, theorem 18.16).
On an integral highest weight representation the KW character is a Jacobi form, closely related to the Witten genus (KL 95). See also at equivariant elliptic cohomology.
Iain Gordon, Infinite-dimensional Lie algebras (2008/9) (pdf
Kefeng Liu, section 2.2 of On modular invariance and rigidity theorems, J. Differential Geom. Volume 41, Number 2 (1995), 247-514 (EUCLID, pdf)
Antony Wassermann, Kac-Moody and Virasoro algebras, course notes (2011) (pdf)