Verma modules and preprojective algebras

Christof Geiss (1) , Bernard Leclerc (2) , Jan Schröer (3)

1 Instituto de Matematicas [México]
2 LMNO - Laboratoire de Mathématiques Nicolas Oresme
3 Department of Pure Mathematics

We give a geometric construction of the Verma modules of a symmetric Kac-Moody Lie algebra in terms of constructible functions on the varieties of nilpotent finite-dimensional modules of the corresponding preprojective algebra.

Mots clés: Kac-Moody algebra; Verma module; preprojective algebra; nilpotent variety

Domaines: Théorie des représentations [math.RT]

Christof Geiss, Bernard Leclerc, Jan Schröer. Verma modules and preprojective algebras. Nagoya Mathematical Journal, 2006, 182, pp.241-258. ⟨hal-00003229v2⟩