nLab
Kac-Weyl character

Contents

Idea

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).

Properties

Jacobi form and relation to Witten genus

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.

References

  • 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)

Revised on March 19, 2014 07:49:04 by Urs Schreiber (89.204.155.252)