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The Support of an Irreducible Lie Algebra Representation

✍ Scribed by Ivan Penkov; Vera Serganova

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
194 KB
Volume
209
Category
Article
ISSN
0021-8693

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✦ Synopsis

We present an explicit description of the α’…-support supp M of any irreducible α’…-locally finite α’„-module M, where α’„ is any finite-dimensional Lie algebra and α’… is an arbitrary nilpotent Lie subalgebra of α’„. If α’… contains a Cartan subalgebra of the semi-simple part of α’„, we reformulate the description of supp M in terms of a lattice L and of the convex hull S of supp M. When α’„ is reductive it is known M M Β² : that supp M is nothing but the intersection of S with the root lattice ⌬ shifted M by an arbitrary element of supp M. Our general description is similar, but the root 2 : lattice ⌬ must be replaced by a certain sublattice L , and supp M may now have M ''holes'' near the boundary of S . The paper is concluded by a detailed discussion M of examples.

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