Generalized Castelnuovo-Mumford regularity for affine Kac-Moody algebras

The graded modules over noncommutative algebras often have minimal free resolutions of infinite length, resulting in infinite Castelnuovo-Mumford regularity. In Kang et al. (2010) [6], we introduced a generalized notion of Castelnuovo-Mumford regularity to overcome this difficulty. In this paper, we compute the generalized Castelnuovo-Mumford regularity for integrable highest weight representations of all affine Kac-Moody algebras. It is shown that the generalized regularity depends only on the type and rank of algebras and the level of representations.