Let 9 be a complex semi-simple Lie algebra. Extending a result of Gerstenhaber on spaces of nilpotent matrices, it is shown that if W c g is a linear subspace of ad nilpotent elements then dim W < i( dim.g -rank g). Similarly, it is shown that the maximal dimension of a linear space of symmetric nil
Complexity of Lie algebra representations and nilpotent elements of the stabilizers of linear forms
β Scribed by Alexander Premet
- Publisher
- Springer-Verlag
- Year
- 1998
- Tongue
- French
- Weight
- 418 KB
- Volume
- 228
- Category
- Article
- ISSN
- 0025-5874
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Given a complex nilpotent finite dimensional Lie algebra of linear transformations, L, in a complex finite dimensional vector space, E, we study the joint spectra Sp(L, E), ,rs, k(L, E), and (r=, k(L , E). We compute them, and we prove that they all coincide with the set of weights of L for E. We al
Let U be a unitary irreducible locally faithful representation of a nilpotent Lie group G, ~ the universal enveloping algebra of G, M a simple module on o//with kernel Ker dU, then there exists an automorphism of q/keeping ker dU invariant such that, after transport of structure, M is isomorphic to