Abstract
We present an explicit description of the h-support suppMof any irreducible h-locally finite g-moduleM, where g is any finite-dimensional Lie algebra and h is an arbitrary nilpotent Lie subalgebra of g. If h contains a Cartan subalgebra of the semi-simple part of g, we reformulate the description of suppMin terms of a latticeL̂Mand of the convex hullSMof suppM. When g is reductive it is known that suppMis nothing but the intersection ofSMwith the root lattice 〈Δ〉 shifted by an arbitrary element of suppM. Our general description is similar, but the root lattice 〈Δ〉 must be replaced by a certain sublatticeL̂M, and suppMmay now have “holes” near the boundary ofSM. The paper is concluded by a detailed discussion of examples.
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