Category of sp(2n)-modules with Bounded Weight Multiplicities

Abstract

Let g be a finite dimensional simple Lie algebra. Denote by B the category of all bounded weight g-modules, i.e. those which are direct sum of their weight spaces and have uniformly bounded weight multiplicities. A result of Fernando shows that infinite-dimensional bounded weight modules exist only for g = sl(n) and g = sp(2n). If g = sp(2n) we show that B has enough projectives if and only if n > 1. In addition, the indecomposable projective modules can be parameterized and described explicitly. All indecomposable objects are described in terms of indecomposable representations of a certain quiver with relations. This quiver is wild for n > 2. For n = 2 we describe all indecomposables by relating the blocks of B to the representations of the ane quiver