Let G be a compact connected semisimple Lie group, Gℂ its complexification and let P be a parabolic subgroup of GC. Let P = L.Ru(P) be the Levi decomposition of P, where L is the Levi component of P and Ru(P) is the unipotent part of P. The group L acts by the adjoint representation on the successive quotients of the central series u(p) = u(0)(p) ⊃ u(1)(p) ⊃ . . . ⊃ u(i)(p) ⊃ . . . ⊃ u(r-1)(p) ⊃ u(r)(p) = 0, where u(p) is the Lie algebra of Ru(P). We determine for each 0 ≤ i ≤ r - 1 the irreducible components Vi(n1, ..., nv) of the adjoint action of L on u(i)(p)/u(i+1)(p).
|Number of pages||4|
|Journal||Bulletin of the Belgian Mathematical Society - Simon Stevin|
|Publication status||Published - Oct 2005|
- Central series
- Irreducible representations
- Parabolic subgroups
ASJC Scopus subject areas